## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

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- I.E. Shparlinski and C.L. Stewart, Counting solvable S-unit equations, 14 pages submitted. Counting solvable S-unit equations (PDF)
- M. Sha, I.E. Shparlinski and C.L. Stewart, On the distribution of multiplicatively dependent vectors, 19 pages submitted.

On the distribution of multiplicatively dependent vectors (PDF) - J-H. Evertse, K. Gyory and C.L. Stewart, Mahler's work on Diophantine equations and subsequent developments, "The Legacy of Kurt Mahler: A Mathematical Selecta",
*Documenta Mathematica*, Extra Vol. Mahler Selecta, (2019), 149-171.

Mahler's work on Diophantine equations and subsequent developments (PDF) - C.L. Stewart and S. Xiao, On the representation of k-free integers by binary forms, 25 pages, to appear in
*Revista Matemática Iberoamericana*.

On the representation of k-free integers by binary forms (PDF) - C.L. Stewart, Multiplicatively dependent vectors with coordinates algebraic numbers,
*Hardy-Ramanujan Journal***42**(2019), 64-69.

Multiplicatively dependent vectors with coordinates algebraic numbers (PDF) - C.L. Stewart and S. Xiao, On the representation of integers by binary forms,
*Mathematische Annalen***375**(2019), 133-163.

On the representation of integers by binary forms (PDF) - M.R. Murty, F. Seguin and C.L. Stewart, A lower bound for the two-variable Artin conjecture and prime divisors of recurrence sequences,
*Journal of Number Theory*,**194**(2019), 8-29.

A lower bound for the two-variable Artin conjecture and prime divisors of recurrence sequences (PDF) - C.L. Stewart, Sets generated by finite sets of algebraic numbers,
*Acta Arithmetica*,**184**(2018), 193-200.

Sets generated by finite sets of algebraic numbers (PDF) - F. Pappalardi, M. Sha, I.E. Shparlinski and C.L. Stewart, On multiplicatively dependent vectors of algebraic numbers,
*Transactions of the A.M.S.*,**370**(2018), 6221-6244.

On multiplicatively dependent vectors of algebraic numbers (PDF) - Jeongsoo Kim and C.L. Stewart, Well spaced integers generated by an infinite set of primes, Proceedings of the A.M.S.,
**143**(2015), 915-923.

Well spaced integers generated by an infinite set of primes (PDF) - O. Robert, C.L. Stewart and G. Tenenbaum, A refinement of the abc conjecture, Bulletin of the London Math. Soc.,
**46**(2014), 1156-1166.

A refinement of the abc conjecture (PDF) - C.L. Stewart, On divisors of Lucas and Lehmer numbers,
*Acta Mathematica*,**211**(2013), 291-314.

On Divisors of Lucas and Lehmer Numbers (PDF). - K. Gyarmati, A. Sárközy and C.L. Stewart, On Legendre symbol lattices, II,
*Uniform Distribution Theory*,**8**(2013), 47-65.

On Legendre symbol lattices, II (PDF). - C.L. Stewart, Exceptional units and cyclic resultants,
*Acta Arithmetica*,**155**(2012), 407-418.

Exceptional units and cyclic resultants (PDF). - F. Beukers and C.L. Stewart, Addendum to "Neighboring powers," Journal of Number Theory 130 (2010), 1571.

Addendum to Neighboring Powers (PDF). - F. Beukers and C.L. Stewart, Neighboring powers, Journal of Number Theory 130 (2010), 660-679.

Neighboring powers (PDF). - C.L. Stewart, Integer points on cubic Thue equations, Comptes rendus Mathematique Acad. Sci. Paris, Ser. I 347 (2009), 715-718.

Integer points on cubic Thue equations (PDF). - K. Gyarmati, A. Sárközy and C.L. Stewart, On Legendre symbol lattices, Uniform Distribution Theory 4 (2009), 81-95.

On Legendre symbol lattices (PDF). - A. Sárközy and C.L. Stewart, Irregularities of sequences relative to long arithmetic progressions, Analytic Number Theory Essays in Honour of Klaus Roth, edited by Chen, Gowers, Halbertstam, Schmidt and Vaughan, Cambridge University Press (2009), 389-401.

Irregularities of sequences relative to long arithmetic progressions (PDF). - C.L. Stewart, Cubic Thue equations with many solutions, International Mathematics Research Notes 2008, rnn040, 11 pages.

Cubic Thue equations with many solutions (PDF). - C.L. Stewart, On sets of integers whose shifted products are powers, J. Combinatorial Theory, Series A, 115 (2008), 662-673.

On sets of integers whose shifted products are powers (PDF). - C.L. Stewart, On heights of multiplicatively dependent algebraic numbers, Acta Arith., 133 (2008), 97-108.

On heights of multiplicatively dependent algebraic numbers (PDF). - H. Maier and C.L. Stewart, On intervals with few prime numbers, J. Reine Angew. Math. 608 (2007), 183-199.

On intervals with few prime numbers (PDF). - A. Sárközy and C.L. Stewart, On pseudorandomness in families of sequences derived from the Legendre symbol, Periodica Math. Hung. 54 (2007), 163-173.

On pseudorandomness in families of sequences derived from the Legendre symbol (PDF). - K. Gyarmati and C.L. Stewart, On powers in shifted products, Glasnik Mat. 42 (2007), 273-279.

On powers in shifted products (PDF).. - C.L. Stewart, On the greatest and least prime factors of $n!+1$, II, Publ. Math. Debrecen, 65 (2004), 461-480.

On the greatest and least prime factors of $n!+1$ (PDF). - J.-H. Evertse, P. Moree, C.L. Stewart and R. Tijdeman, Multivariate Diophantine equations with many solutions, Acta Arith., 107 (2003), 103-125.

Multivariate Diophantine equations with many solutions (PDF). - K. Gyarmati, A. Sárközy and C.L. Stewart, On sums which are powers, Acta Math. Hung., 99 (2003), 1-24.

On sums which are powers (PDF). - K. Gyarmati, A. Sárközy and C.L. Stewart, On shifted products which are powers, Mathematika, 49 (2002), 227-230.

On shifted products which are powers (PDF). - C.L. Stewart and Kunrui Yu, On the abc conjecture, II, Duke Math. J. 108 (2001), 169-181.

On the abc conjecture, II (PDF). - C.L. Stewart, A. Sárközy - a retrospective on the occasion of his sixtieth birthday, Periodica Math. Hung. 42 (2001), 1-16.

A. Sárközy - a retrospective on the occasion of his sixtieth birthday (PDF). - C.L. Stewart, On the greatest prime factor of integers of the form ab+1, Periodica Math. Hung. 43 (2001), 81-91.

On the greatest prime factor of integers of the form ab+1 (PDF). - A. Sárközy and C.L. Stewart, On prime factors of integers of the form ab+1, Publ. Math. Debrecen 56 (2000), 559-573.

On prime factors of integers of the form ab+1 (PDF). - J. Rivat, A. Sárközy and C.L. Stewart, Congruence properties of the Omega-function on sumsets, Illinois J. Math., 43 (1999), 1-18.

Congruence properties of the Omega-function on sumsets (PDF). - W.M. Schmidt and C.L. Stewart, Congruences, trees and p-adic integers, Transactions of the A.M.S., 349 (1997), 605-639.

Congruences, trees and p-adic integers, Transactions of the A.M.S. (PDF). - C.L. Stewart and R.Tijdeman, On the greatest prime factor of (ab+1) (ac+1)(bc+1), Acta Arith., 79 (1997), 93-101.

On the greatest prime factor of (ab+1) (ac+1)(bc+1) (PDF). - C.L. Stewart, Second thoughts on some topics from Diophantine approximation and analytic number theory, Canadian Mathematical Society 1945-1995, Volume 3, Invited Papers, edited by J.B. Carrell and R. Murty, University of Toronto Press (1996), 247-266.

Second thoughts on some topics from Diophantine approximation and analytic number theory (PDF). - K. Gyory, A. Sárközy and C.L. Stewart, On the number of prime factors of integers of the form ab+1, Acta Arith., 74 (1996), 365-385.

On the number of prime factors of integers of the form ab+1 (PDF). - C.L. Stewart and J. Top, On ranks of twists of elliptic curves and power-free values of binary forms, Journal of the American Math. Soc. 8 (1995), 943-973.

On ranks of twists of elliptic curves and power-free values of binary forms (PDF). - A. Sárközy and C.L. Stewart, On divisors of sums of integers V, Pacific Journal of Mathematics 166 (1994), 373-384.

On divisors of sums of integers V (PDF). - A. Sárközy and C.L. Stewart, On the average value for the number of divisors of sums a+b, Illinois Journal of Math. 38 (1994), 1-18.

On the average value for the number of divisors of sums a+b (PDF). - P. Erdos, A. Sárközy and C.L. Stewart, On prime factors of subset sums, Journal of the London Math. Soc. 49 (2) (1994), 209-218.

On prime factors of subset sums (PDF). - P. Erdos, C. Pomerance, A. Sárközy and C.L. Stewart, On elements of sumsets with many prime factors, J. Number Theory 44 (1993), 93-104.

On elements of sumsets with many prime factors (PDF). - C.L. Stewart, On the number of solutions of polynomial congruences, C.R. Math. Rep. Acad. Sci. Canada, 13 (1991), 271-273.

On the number of solutions of polynomial congruence (PDF). - C.L. Stewart and Kunrui Yu, On the abc conjecture, Math. Annalen, 291 (1991), 225-230.

On the abc conjecture (PDF). - C.L. Stewart, On the number of solutions of polynomial congruences and Thue equations, Journal of the American Math. Soc., 4 (1991), 793-835.

On the number of solutions of polynomial congruences and Thue equations (PDF). - P. Moree and C.L. Stewart, Some Ramanujan-Nagell equations with many solutions, Nederl. Akad. Wetensch. Proc. Ser. A. (1990), 465-472.

Some Ramanujan-Nagell equations with many solutions (PDF). - A. Sárközy and C.L. Stewart, On exponential sums over prime numbers, J. Australian Math. Soc. (Series A), 46 (1989), 423-437.

On exponential sums over prime numbers (PDF). - A. Sárközy and C.L. Stewart, On divisors of sums of integers IV, Canadian J. Math. 40 (1988), 788-816.

On divisors of sums of integers IV (PDF). - J.H. Evertse, K, Gyory, C.L. Stewart and R. Tijdeman, On S-unit equations in two unknowns, Inventiones Math. 92 (1988), 461-477.

On S-unit equations in two unknowns (PDF). - K. Gyory, C.L. Stewart and R. Tijdeman, On prime factors of sums of integers III, Acta Arith. 49 (1988), 307-312.

On prime factors of sums of integers III (PDF). - P. Erdos, C.L. Stewart and R. Tijdeman, Some Diophantine equations with many solutions, Compositio Math. 66 (1988), 37-56.

Some Diophantine equations with many solutions (PDF). - C. Pomerance, A. Sárközy and C.L. Stewart, On divisors of sums of integers III, Pacific J. Math. 133 (1988), 363-379.

On divisors of sums of integers III (PDF). - T.N. Shorey and C.L. Stewart, Pure powers in recurrence sequences and some related Diophantine equations, J. Number Theory 27 (1987), 324-352.

Pure powers in recurrence sequences and some related Diophantine equations (PDF). - A. Sárközy and C.L. Stewart, On irregularities of distribution in shifts and dilations of integer sequences I, Math. Annalen 276 (1987), 353-364.

On irregularities of distribution in shifts and dilations of integer sequences I (PDF). - C.L. Stewart and R. Tijdeman, On the Oesterlé-Masser conjecture, Monatshefte Math. 102 (1986), 251-257.

On the Oesterlé-Masser conjecture (PDF). - A. Sárközy and C.L. Stewart, On divisors of sums of integers II, J. reine angew. Math. 365 (1986), 171-191.

On divisors of sums of integers II (PDF). - A. Sárközy and C.L. Stewart, On divisors of sums of integers I, Acta Math. Hung. 48 (1986), 147-154.

On divisors of sums of integers I (PDF). - C.L. Stewart, Some remarks on prime divisors of sums of integers, Sém. Théorie des Nombres, Progress in Math. 63, Birkhauser (1986), 217-223.

Some remarks on prime divisors of sums of integers, Sém. Théorie des Nombres (PDF). - K. Gyory, C.L. Stewart and R. Tijdeman, On prime factors of sums of integers I, Compositio Math. 59 (1986), 81-88.

On prime factors of sums of integers I (PDF). - C.L. Stewart, On the greatest prime factor of terms of a linear recurrence sequence, Rocky Mountain Journal of Mathematics 15 (1985), 603-612.

On the greatest prime factor of terms of a linear recurrence sequence (PDF). - C.L. Stewart, On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers III, J. London Math. Soc. 28(2) (1983), 211-217.

On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers III (PDF). - C.L. Stewart and R. Tijdeman, On density-difference sets of sequences of integers, Studies in Pure Mathematics - to the memory of Paul Turan, Birkhauser Verlag and the Publishing House of the Hungarian Academy of Sciences (1983), 701-710.

On density-difference sets of sequences of integers (PDF). - T.N. Shorey and C.L. Stewart, On the Diophantine equation ax^{2t} +bx^{ty} +cy^{2} = d and pure powers in recurrence sequences, Math. Scandinavica 52 (1983), 24-36.

On the Diophantine equation ax^{2t} +bx^{ty} +cy^{2} = d and pure powers in recurrence sequences (PDF). - C.L. Stewart, On some Diophantine equations and related linear recurrence sequences, Sém. Delange-Pisot-Poitou, (1980-81), Progress in Mathematics, Birkhauser Verlag 22 (1982), 317-321.

On some Diophantine equations and related linear recurrence sequences (PDF). - C.L. Stewart, On divisors of terms of linear recurrence sequences, J. reine angew. Math. 333 (1982), 12-31.

On divisors of terms of linear recurrence sequences (PDF). - T.N. Shorey and C.L. Stewart, On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers II, J. London Math. Soc. 23(2) (1981), 17-23.

On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers II (PDF). - C.L. Stewart, On the representation of an integer in two different bases, J. reine angew. Math. 219 (1980), 63-72.

On the representation of an integer in two different bases (PDF). - C.L. Stewart and R. Tijdeman, On infinite-difference sets, Canadian J. Math. 31 (1979), 897-910.

On infinite-difference sets (PDF). - C.L. Stewart, Algebraic integers whose conjugates lie near the unit circle, Bull. Soc. Math. France 106 (1978), 169-176.

Algebraic integers whose conjugates lie near the unit circle (PDF). - C.L. Stewart, A note on the Fermat equation, Mathematika 24 (1977), 130-132.

A note on the Fermat equation (PDF). - A. Baker and C.L. Stewart, Further aspects of transcendence theory, Astérisque 41-42 (1977), 153-163.

Further aspects of transcendence theory (PDF). - C.L. Stewart, On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers, Proc. London Math. Soc. 35(3) (1977), 425-447.

On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers (PDF). - P. Erdos and C.L. Stewart, On the greatest and least prime factors of n!+1, J. London Math. Soc. 13(2) (1976), 513-519.

On the greatest and least prime factors of n!+1 (PDF). - C.L. Stewart, The greatest prime factor of a^{n}-b^{n}, Acta Arith. 26 (1975), 427-433.

The greatest prime factor of a^{n}-b^{n} (PDF).

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Indigenous Initiatives Office.