Department of Mathematics and Statistics at the Faculty of Science
University of Calgary
UofC Navigation
Hugh Williams
- Professor
- Director - ISPIA
- Pure Mathematics
Research Interests
Algebra and Number Theory:
General:
Currently Teaching
Not currently teaching any courses.
Publications
Book
- Williams, Hugh. Solving the {P}ell equation A K Peters, 2002. 397-435.
- Teske, Edlyn and Williams, Hugh. A note on {S}hanks's chains of primes 1838. Springer, 2000. 563-580.
- Stein, Andreas and Williams, Hugh. An improved method of computing the regulator of a real quadratic function field 1423. Springer, 1998. 607-620.
- Teske, E. and Williams, Hugh. A problem concerning a character sum (extended abstract) 1423. Springer, 1998. 351-357.
- Williams, Hugh. \'{E}douard {L}ucas and primality testing , John Wiley \& Sons Inc., 1998. x+525.
- Buchmann, Johannes , Thiel, Christoph and Williams, Hugh. Short representation of quadratic integers 325. Kluwer Acad. Publ., 1995. 159-185.
- Williams, Hugh and Shallit, J. O.. Factoring integers before computers 48. Amer. Math. Soc., 1994. 481-531.
- Louboutin, S. , Mollin, Richard and Williams, Hugh. Class groups of exponent two in real quadratic fields , Oxford Univ. Press, 1993. 499-513.
- Mollin, Richard and Williams, Hugh. On a solution of a class number two problem for a family of real quadratic fields de Gruyter, 1991. 95-101.
- Mollin, Richard and Williams, Hugh. Powers of {$2,$} continued fractions, and the class number one problem for real quadratic fields {${\bf Q}(\sqrt d),$} with {$d\equiv 1\pmod 8$} World Sci. Publishing, 1991. 505-516.
- Buchmann, Johannes A. and Williams, Hugh. A key exchange system based on real quadratic fields (extended abstract) 435. Springer, 1990. 335-343.
- Mollin, Richard and Williams, Hugh. Solution of the class number one problem for real quadratic fields of extended {R}ichaud-{D}egert type (with one possible exception) de Gruyter, 1990. 417-425.
- Buchmann, Johannes A., D{\"u}llmann, Stephan and Williams, Hugh. On the complexity and efficiency of a new key exchange system 434. Springer, 1990. 597-616.
- Mollin, Richard and Williams, Hugh. Class number problems for real quadratic fields 154. Cambridge Univ. Press, 1990. 177-195.
- Stephens, A. J. and Williams, Hugh. An open architecture number sieve 154. Cambridge Univ. Press, 1990. 38-75.
- Buchmann, Johannes and Williams, Hugh. Quadratic fields and cryptography 154. Cambridge Univ. Press, 1990. 9-25.
- Mollin, Richard and Williams, Hugh. Class number one for real quadratic fields, continued fractions and reduced ideals 265. Kluwer Acad. Publ., 1989. 481-496.
- Buchmann, Johannes and Williams, Hugh. On the existence of a short proof for the value of the class number and regulator of a real quadratic field 265. Kluwer Acad. Publ., 1989. 327-345.
- Stephens, A. J. and Williams, Hugh. Some computational results on a problem of {E}isenstein de Gruyter, 1989. 869-886.
- Mollin, Richard and Williams, Hugh. Prime producing quadratic polynomials and real quadratic fields of class number one de Gruyter, 1989. 654-663.
- Williams, Hugh. An {$M\sp 3$} public-key encryption scheme 218. Springer, 1986. 358-368.
- Williams, Hugh. Some public-key crypto-functions as intractable as factorization (extended abstract) 196. Springer, 1985. 66-70.
- Williams, Hugh. An overview of factoring Plenum, 1984. 71-80.
- Williams, Hugh. Computationally ``hard'' problems as a source for cryptosystems 69. Westview, 1982. 11-39.
- Stanton, R. G. and Williams, Hugh. Computation of some number-theoretic coverings 884. Springer, 1981. 8-13.
- Williams, Hugh. A generalization of the {F}ibonacci numbers Louisiana State Univ., 1970. 340-356.
Book Chapter
- Jacobson, Michael, Scheidler, Renate and Williams, Hugh. The efficiency and security of a real quadratic field-based key exchange protocol Berlin: de Gruyter & Co. Publishers, 2001. 89-112.
Conference Proceedings
- Wooding, Kjell and Williams, Hugh. Doubly-focused enumeration of Pseudosquares and Pseudocubes 4076 Springer-Verlag, 2006. 208-221.
- Scheidler, Renate, Buchmann, Johannes and Williams, Hugh. Implementation of a key exchange protocol using real quadratic fields (extended abstract) 1991.
Journal Paper
- Jacobson, M.J., Scheidler, Renate and Williams, Hugh. An improved real quadratic field based key exchange procedure 19.2 2006. 211-239.
- Poorten, A. J., Riele, H. J. J. and Williams, Hugh. Corrigenda and addition to: ``{C}omputer verification of the {A}nkeny-{A}rtin-{C}howla conjecture for all primes less than {$100\,000\,000\,000$}'' [{M}ath.\ {C}omp.\ {\bf 70} (2001), no. 235, 1311-1328; \refmr {MR}1709160 (2001j:11125)\endrefmr] 72.241 2003. 521-523 (electronic).
- Jacobson, Jr. and Williams, Hugh. New quadratic polynomials with high densities of prime values 72.241 2003. 499-519 (electronic).
- Riele, Herman and Williams, Hugh. New computations concerning the {C}ohen-{L}enstra heuristics 12.1 2003. 99-113.
- Jacobson, Jr. and Williams, Hugh. Modular arithmetic on elements of small norm in quadratic fields 27.1-2 2002. 93-110.
- Sellers, James A. and Williams, Hugh. On the infinitude of composite {NSW} numbers 40.3 2002. 253-254.
- Poorten, A. J., Riele, H. J. J. and Williams, Hugh. Computer verification of the {A}nkeny-{A}rtin-{C}howla conjecture for all primes less than {$100\,000\,000\,000$} 70.235 2001. 1311-1328.
- Stein, Andreas and Williams, Hugh. Explicit primality criteria for {$(p-1)p\sp n-1$} 69.232 2000. 1721-1734.
- Granville, Andrew , Mollin, Richard and Williams, Hugh. An upper bound on the least inert prime in a real quadratic field 52.2 2000. 369-380.
- Jacobson, Jr. and Williams, Hugh. The size of the fundamental solutions of consecutive {P}ell equations 9.4 2000. 631-640.
- Williams, Hugh. A number theoretic function arising from continued fractions 38.3 2000. 201-211.
- Poorten, A. J. and Williams, Hugh. On certain continued fraction expansions of fixed period length 89.1 1999. 23-35.
- Teske, Edlyn and Williams, Hugh. A problem concerning a character sum 8.1 1999. 63-72.
- Stein, Andreas and Williams, Hugh. Some methods for evaluating the regulator of a real quadratic function field 8.2 1999. 119-133.
- Williams, Hugh. Daniel {S}hanks (1917-1996) 66.219 1997. 929-934.
- Lukes, Richard F., Scheidler, Renate and Williams, Hugh. Further tabulation of the Erdos-Selfridge function 66.220 1997. 1709-1717.
- Lukes, R. F., Patterson, C. D. and Williams, Hugh. Some results on pseudosquares 65.213 John Wiley & Sons Inc., 1996. 361-372, S25-S27.
- Bach, Eric , Lukes, Richard , Shallit, Jeffrey and Williams, Hugh. Results and estimates on pseudopowers 65.216 John Wiley & Sons Inc., 1996. 1737-1747.
- Scheidler, Renate, Stein, Andreas and Williams, Hugh. Key-exchange in real quadratic congruence function fields 7.1-2 1996. 153-174.
- Mollin, Richard and Williams, Hugh. Corrigenda for: ``{A} conjecture of {S}. {C}howla via the generalized {R}iemann hypothesis'' [{P}roc.\ {A}mer.\ {M}ath.\ {S}oc. {\bf 102} (1988), no.\ 4, 794-796; \refmr {MR}0934844 (89d:11090)\endrefmr] 123.3 1995. 975.
- Mollin, Richard and Williams, Hugh. Proof, disproof and advances concerning certain conjectures on real quadratic fields {$\bold Q(\sqrt{N\sp 2+4})$} 47.5 1995. 1023-1036.
- Williams, Hugh. Some generalizations of the {$S\sb n$} sequence of {S}hanks 69.3 John Wiley & Sons Inc., 1995. 199-215.
- Lukes, R. F., Patterson, C. D. and Williams, Hugh. Numerical sieving devices: their history and some applications 13.1 John Wiley & Sons Inc., 1995. 113-139.
- Jacobson, Jr. , Lukes, Richard F. and Williams, Hugh. An investigation of bounds for the regulator of quadratic fields 4.3 John Wiley & Sons Inc., 1995. 211-225.
- Shallit, Jeffrey , Williams, Hugh and Morain, Fran . Discovery of a lost factoring machine 17.3 John Wiley & Sons Inc., 1995. 41-47.
- Scheidler, Renate and Williams, Hugh. A public-key cryptosystem utilizing cyclotomic fields 6.2 1995. 117-131.
- Mollin, Richard, Poorten, A. J. and Williams, Hugh. Halfway to a solution of {$X\sp 2-DY\sp 2=-3$} 6.2 1994. 421-457.
- Fung, G. W. and Williams, Hugh. Errata: ``{O}n the computation of a table of complex cubic fields with discriminant {$D>-10\sp 6$}'' [{M}ath.\ {C}omp.\ {\bf 55} (1990), no.\ 191, 313-325; \refmr {MR}1023760 (90m:11155)\endrefmr] 63.207 John Wiley & Sons Inc., 1994. 433.
- Mollin, Richard and Williams, Hugh. Quadratic residue covers for certain real quadratic fields 62.206 1994. 885-897.
- Scheidler, Renate, Buchmann, Johannes and Williams, Hugh. A key exchange protocol using real quadratic fields 7.3 1994. 171-199.
- Mollin, Richard and Williams, Hugh. Classification and enumeration of real quadratic fields having exactly one noninert prime less than a {M}inkowski bound 36.1 1993. 108-115.
- Williams, Hugh. How was {$F\sb 6$} factored? 61.203 John Wiley & Sons Inc., 1993. 463-474.
- Mollin, Richard and Williams, Hugh. Computation of the class number of a real quadratic field 41. 1992. 259-308.
- Mollin, Richard and Williams, Hugh. A complete generalization of {Y}okoi's {$p$}-invariants 63.2 1992. 285-294.
- Mollin, Richard and Williams, Hugh. On the period length of some special continued fractions 4.1 1992. 19-42.
- Mollin, Richard and Williams, Hugh. On real quadratic fields of class number two 59.200 1992. 625-632.
- Louboutin, S. , Mollin, Richard and Williams, Hugh. Class numbers of real quadratic fields, continued fractions, reduced ideals, prime-producing quadratic polynomials and quadratic residue covers 44.4 1992. 824-842.
- Fung, Gilbert , Granville, Andrew and Williams, Hugh. Computation of the first factor of the class number of cyclotomic fields 42.3 John Wiley & Sons Inc., 1992. 297-312.
- Mollin, Richard and Williams, Hugh. Consecutive powers in continued fractions 61.3 1992. 233-264.
- Scheidler, Renate and Williams, Hugh. A method of tabulating the number-theoretic function g(k) 59.199 1992. 251-257.
- Williams, Hugh. Some formulas concerning the fundamental unit of a real quadratic field 92.1-3 1991. 431-440.
- Mollin, Richard and Williams, Hugh. Corrigenda for: ``{S}olution of a problem of {Y}okoi'' [{P}roc.\ {J}apan {A}cad.\ {S}er.\ {A} {M}ath.\ {S}ci.\ {\bf 66} (1990), no.\ 6, 141-145; \refmr {MR}1065792 (91k:11094)\endrefmr] 67.7 1991. 253.
- Mollin, Richard and Williams, Hugh. On the divisor function and class numbers of real quadratic fields. {III} 67.10 1991. 338-342.
- Mollin, Richard and Williams, Hugh. Affirmative solution of a conjecture related to a sequence of {S}hanks 67.3 1991. 70-72.
- Mollin, Richard and Williams, Hugh. On a determination of real quadratic fields of class number one and related continued fraction period length less than {$25$} 67.1 1991. 20-25.
- Buchmann, Johannes A. and Williams, Hugh. Some remarks concerning the complexity of computing class groups of quadratic fields 7.3 1991. 311-315.
- Fung, Gilbert W. and Williams, Hugh. On the computation of a table of complex cubic fields with discriminant {$D>-10\sp 6$} 55.191 1990. 313-325.
- Fung, G. W. and Williams, Hugh. Quadratic polynomials which have a high density of prime values 55.191 1990. 345-353.
- Buchmann, J. , Sands, J. W. and Williams, Hugh. {$p$}-adic computation of real quadratic class numbers 54.190 1990. 855-868.
- Fung, G. W., Str{\"o}her, H. , Williams, Hugh and Zimmer, H. G.. Torsion groups of elliptic curves with integral {$j$}-invariant over pure cubic fields 36.1 1990. 12-45.
- Mollin, Richard and Williams, Hugh. Solution of a problem of {Y}okoi 66.6 1990. 141-145.
- Williams, Hugh. The period length of {V}orono\u\i's algorithm for certain cubic orders 37.3-4 1990. 245-265.
- Mollin, Richard and Williams, Hugh. Continued fractions of period five and real quadratic fields of class number one 56.1 1990. 55-63.
- Williams, Hugh. Eisenstein's problem and continued fractions 37. 1990. 145-157.
- Mollin, Richard and Williams, Hugh. Quadratic nonresidues and prime-producing polynomials 32.4 1989. 474-478.
- Buchmann, Johannes and Williams, Hugh. On the computation of the class number of an algebraic number field 53.188 1989. 679-688.
- Mollin, Richard and Williams, Hugh. Period four and real quadratic fields of class number one 65.4 1989. 89-93.
- Mollin, Richard and Williams, Hugh. Real quadratic fields of class number one and continued fraction period less than six 11.2 1989. 51-56.
- Mollin, Richard and Williams, Hugh. A conjecture of {S}. {C}howla via the generalized {R}iemann hypothesis 102.4 1988. 794-796.
- Williams, Hugh. Corrigenda: ``{C}omputation of the class number and class group of a complex cubic field'' [{M}ath.\ {C}omp.\ {\bf 45} (1985), no.\ 171, 223-231; \refmr {MR}0790655 (86m:11078)\endrefmr] by {G}.\ {W}.\ {D}ueck and {W}illiams 50.182 1988. 655-657.
- Stephens, A. J. and Williams, Hugh. Computation of real quadratic fields with class number one 51.184 1988. 809-824.
- Stephens, A. J. and Williams, Hugh. Some computational results on a problem concerning powerful numbers 50.182 1988. 619-632.
- Buchmann, Johannes and Williams, Hugh. On the infrastructure of the principal ideal class of an algebraic number field of unit rank one 50.182 1988. 569-579.
- Mollin, Richard and Williams, Hugh. On prime valued polynomials and class numbers of real quadratic fields 112. 1988. 143-151.
- Williams, Hugh. A note on the primality of {$6\sp {2\sp n}+1$} and {$10\sp {2\sp n}+1$} 26.4 1988. 296-305.
- Buchmann, Johannes and Williams, Hugh. A key-exchange system based on imaginary quadratic fields 1.2 1988. 107-118.
- Barrucand, Pierre , Loxton, John and Williams, Hugh. Some explicit upper bounds on the class number and regulator of a cubic field with negative discriminant 128.2 1987. 209-222.
- Williams, Hugh and Wunderlich, M. C.. On the parallel generation of the residues for the continued fraction factoring algorithm 48.177 1987. 405-423.
- Williams, Hugh. Effective primality tests for some integers of the forms {$A5\sp n-1$} and {$A7\sp n-1$} 48.177 1987. 385-403.
- Buchmann, Johannes and Williams, Hugh. On principal ideal testing in totally complex quartic fields and the determination of certain cyclotomic constants 48.177 1987. 55-66.
- Buchmann, Johannes and Williams, Hugh. On principal ideal testing in algebraic number fields 4.1 1987. 11-19.
- Williams, Hugh. The spacing of the minima in certain cubic lattices 124.2 1986. 483-496.
- Williams, Hugh and Dubner, Harvey . The primality of {$R1031$} 47.176 1986. 703-711.
- Kurtz, G. C., Shanks, Daniel and Williams, Hugh. Fast primality tests for numbers less than $50cdot 10sp 9$ 46.174 1986. 691-701.
- Tennenhouse, M. and Williams, Hugh. A note on class-number one in certain real quadratic and pure cubic fields 46.173 1986. 333-336.
- Dueck, G. and Williams, Hugh. Computation of the class number and class group of a complex cubic field 45.171 1985. 223-231.
- Patterson, C. D. and Williams, Hugh. Some periodic continued fractions with long periods 44.170 1985. 523-532.
- Williams, Hugh. Continued fractions and number-theoretic computations 15.2 1985. 621-655.
- Williams, Hugh. Some public-key crypto-functions as intractable as factorization 9.3 1985. 223-237.
- Williams, Hugh. A note on the period length of the continued fraction expansion of certain {$\sqrt D$} 28. 1985. 201-209.
- Williams, Hugh. On mid-period criteria for the nearest integer continued fraction expansion of {$\sqrt D$} 27. 1985. 169-185.
- Williams, Hugh and Dueck, G. W.. An analogue of the nearest integer continued fraction for certain cubic irrationalities 42.166 1984. 683-705.
- Williams, Hugh. Factoring on a computer 6.3 1984. 29-36.
- Seah, Eric , Washington, Lawrence C. and Williams, Hugh. The calculation of a large cubic class number with an application to real cyclotomic fields 41.163 1983. 303-305.
- Williams, Hugh, Dueck, G. W. and Schmid, B. K.. A rapid method of evaluating the regulator and class number of a pure cubic field 41.163 1983. 235-286.
- Patterson, C. D. and Williams, Hugh. A report on the {U}niversity of {M}anitoba {S}ieve {U}nit 37. 1983. 85-98.
- Williams, Hugh. A note on the {F}ibonacci quotient {$F\sb{p-\varepsilon }/p$} 25.3 1982. 366-370.
- Williams, Hugh. A class of primality tests for trinomials which includes the {L}ucas-{L}ehmer test 98.2 1982. 477-494.
- Williams, Hugh. Corrigendum: ``{S}ome primes with interesting digit patterns'' [{M}ath. {C}omp. {\bf 32} (1978), no. 144, 1306-1310;\ {MR} {\bf 58} \#484] 39.160 1982. 759.
- Baillie, Robert , Cormack, G. and Williams, Hugh. Corrigenda: ``{T}he problem of {S}ierpi\'nski concerning {$k\cdot 2\sp{n}+1$}'' [{M}ath. {C}omp. {\bf 37} (1981), no. 155, 229-231] 39.159 1982. 308.
- Williams, Hugh. A {$p+1$} method of factoring 39.159 1982. 225-234.
- Williams, Hugh. Determination of principal factors in {${\scr Q}(\sqrt{D})$} and {${\scr Q}(\root 3\of D)$} 38.157 1982. 261-274.
- Williams, Hugh. The influence of computers in the development of number theory 8.2 1982. 75-93.
- Shanks, Daniel and Williams, Hugh. Gunderson's function in {F}ermat's last theorem 36.153 1981. 291-295.
- Baillie, Robert , Cormack, G. and Williams, Hugh. The problem of {S}ierpi\'nski concerning {$k\cdot 2\sp{n}+1$} 37.155 1981. 229-231.
- Williams, Hugh. Some results concerning {V}orono\u\i 's continued fraction over {${\bf Q}(\root 3\of{D})$} 36.154 1981. 631-652.
- Williams, Hugh. A numerical investigation into the length of the period of the continued fraction expansion of {$\sqrt{D}$} 36.154 1981. 593-601.
- Williams, Hugh. The primality of certain integers of the form {$2Ar\sp{n}-1$} 39.1 1981. 7-17.
- Newman, Morris , Shanks, Daniel and Williams, Hugh. Simple groups of square order and an interesting sequence of primes 38.2 1980/81. 129-140.
- Williams, Hugh. Improving the speed of calculating the regulator of certain pure cubic fields 35.152 1980. 1423-1434.
- Cormack, G. V. and Williams, Hugh. Some very large primes of the form {$k\cdot 2\sp{m}+1$} 35.152 1980. 1419-1421.
- Williams, Hugh, Cormack, G. and Seah, E. . Calculation of the regulator of a pure cubic field 34.150 1980. 567-611.
- Williams, Hugh. Some results concerning the nearest integer continued fraction expansion of {$\surd D$} 315. 1980. 1-15.
- Williams, Hugh. A modification of the {RSA} public-key encryption procedure 26.6 1980. 726-729.
- Purdy, G. , Terras, R. , Terras, A. and Williams, Hugh. Graphing {$L$}-functions of {K}ronecker symbols in the real part of the critical strip 47.2-4 1979. 101-131 (1985).
- Williams, Hugh and Shanks, Daniel . A note on class-number one in pure cubic fields 33.148 1979. 1317-1320.
- Williams, Hugh and Buhr, P. A.. Calculation of the regulator of {${\bf Q}(\surd D)$} by use of the nearest integer continued fraction algorithm 33.145 1979. 369-381.
- Williams, Hugh. Errata: ``{C}ertain pure cubic fields with class-number one'' [{M}ath. {C}omp. {\bf 31} (1977), no. 138, 578-580;\ {MR} {\bf 55} \#5578] 33.146 1979. 847-848.
- Diaz, F. , Shanks, Daniel and Williams, Hugh. Quadratic fields with {$3$}-rank equal to {$4$} 33.146 1979. 836-840.
- Williams, Hugh and Seah, E. . Some primes of the form {$(a\sp{n}-1)/(a-1)$} 33.148 1979. 1337-1342.
- Williams, Hugh and Schmid, B. . Some remarks concerning the {M}.{I}.{T}. public-key cryptosystem 19.4 1979. 525-538.
- Williams, Hugh. Some properties of a special set of recurring sequences 77.1 1978. 273-285.
- Williams, Hugh. Some primes with interesting digit patterns 32.144 1978. 1306-1310.
- Williams, Hugh and Holte, R. . Some observations on primality testing 32.143 1978. 905-917.
- Williams, Hugh. Primality testing on a computer 5. 1978. 127-185.
- Williams, Hugh. On numbers analogous to the {C}armichael numbers 20.1 1977. 133-143.
- Williams, Hugh. Certain pure cubic fields with class-number one 31.138 1977. 578-580.
- Buell, D. A., Williams, Hugh and Williams, K. S.. On the imaginary bicyclic biquadratic fields with class-number {$2$} 31.140 1977. 1034-1042.
- Matthew, G. and Williams, Hugh. Some new primes of the form {$k\cdot 2\sp{n}+1$} 31.139 1977. 797-798.
- Williams, Hugh and Holte, R. . Computation of the solution of {$x\sp{3}+Dy\sp{3}=1$} 31.139 1977. 778-785.
- Williams, Hugh. Properties of some functions similar to {L}ucas functions 15.2 1977. 97-112.
- Williams, Hugh. Some results on fundamental units in cubic fields 286/287. 1976. 75-85.
- Stanton, R. G., Sudler, Jr. and Williams, Hugh. An upper bound for the period of the simple continued fraction for {$\sqrt{D}$} 67.2 1976. 525-536.
- Williams, Hugh and Broere, J. . A computational technique for evaluating {$L(1,\chi )$} and the class number of a real quadratic field 30.136 1976. 887-893.
- Williams, Hugh and Judd, J. S.. Some algorithms for prime testing using generalized {L}ehmer functions 30.136 1976. 867-886.
- Williams, Hugh and Judd, J. S.. Determination of the primality of {$N$} by using factors of {$N\sp{2}\pm 1$} 30.133 1976. 157-172.
- Barrucand, Pierre , Williams, Hugh and Baniuk, L. . A computational technique for determining the class number of a pure cubic field 30.134 1976. 312-323.
- Williams, Hugh. A generalization of {L}ehmer's functions 29.4 1976. 315-341.
- Stanton, R. G. and Williams, Hugh. An application of combinatorics in number theory 1.1 1976. 321-330.
- Williams, Hugh. The rank of apparition of a generalized {F}ibonacci sequence 13.3 1975. 240-242.
- Williams, Hugh. On {F}ibonacci numbers of the form {$k\sp{2}+1$} 13.3 1975. 213-214.
- Williams, Hugh and Zarnke, C. R.. Some algorithms for solving a cubic congruence modulo {$p$} 6. 1974. 285-306.
- Williams, Hugh. The quadratic character of a certain quadratic surd 5. 1974. 49-55.
- Williams, Hugh and Zarnke, C. R.. Computer calculation of units in cubic fields 1973. 433-468. Congressus Numerantium, No. VII.
- Williams, Hugh and Zarnke, C. R.. Computer solution of the {D}iophantine equation {$x\sp{2}-dy\sp{4}=-1$} 1973. 405-416. Congressus Numerantium, No. VII.
- Williams, Hugh and Zarnke, C. R.. Computation of the solutions of the {D}iophantine equation {$x\sp{2}-dy\sp{4}=1$} 1972. 463-483.
- Beach, B. D. and Williams, Hugh. A numerical investigation of the {D}iophantine equation {$x\sp{2}-dy\sp{2}=-1$} 1972. 37-68.
- Williams, Hugh. Some algorithms for solving {$x\sp{q}\equiv N$} {$({\rm mod}\ p)$} 1972. 451-462.
- Williams, Hugh. The primality of {$N=2A3\sp{n}-1$} 15. 1972. 585-589.
- Williams, Hugh and Zarnke, C. R.. Some prime numbers of the forms {$2A3\sp{n}+1$} and {$2A3\sp{n}-1$} 26. 1972. 995-998.
- Williams, Hugh. On a generalization of the {L}ucas functions 20. 1972. 33-51.
- Williams, Hugh. Fibonacci numbers obtained from {P}ascal's triangle with generalizations 10.4 1972. 405-412.
- Williams, Hugh. An algorithm for determining certain large primes 1971. 533-556.
- Gryte, D. G., Kingsley, R. A. and Williams, Hugh. On certain forms of {F}ibonacci numbers 1971. 339-344.
- Beach, B. D. and Williams, Hugh. Some computer results on periodic continued fractions 1971. 133-146.
- Beach, B. D., Williams, Hugh and Zarnke, C. R.. Some computer results on units in quadratic and cubic fields 1971. 609-648.
- Williams, Hugh and Zarnke, C. R.. Computation of the solutions of the {D}iophantine equation {$x\sp{3}+dy\sp{3}=1$} 1971. 671-676.
- Beach, B. D. and Williams, Hugh. A computer algorithm for determining the solution of the {D}iophantine equation {$x\sp{4}-dy\sp{4}=1$} 1971. 663-670. Dept. Comput. Sci., Univ.
- Williams, Hugh. Some properties of the general {L}ucas polynomials 21. 1971. 91-93, 82.
- Williams, Hugh. Note on a diophantine equation 25. 1970. 123-125.
- Williams, Hugh and Zarnke, C. R.. A report on prime numbers of the forms {$M=(6a+1)2\sp{2m-1}-1$} and {$M\sp{\prime} =(6a-1)2\sp{2m}-1$} 22. 1968. 420-422.
- Stanton, R. G., Williams, Hugh and Zarnke, C. R.. A packing problem 10. 1967. 287-297.
Research Groups
Degrees
- 1966 - B.Sc. (Honours) - University of Waterloo
- 1967 - M.Math - University of Waterloo
- 1969 - Ph.D. - University of Waterloo
Students
Ph.D. Students:
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