Michael A. Bennett

Publication List


1993

[1] M. A. Bennett, Fractional parts of powers of rational numbers, Math. Proc. Cambridge Philos. Soc. 114 (1993), 191-201

[2] M. A. Bennett, Effective lower bounds for the fractional parts of powers of a dense set of rationals, C. R. Math. Rep. Acad. Sci. Canada, XV (5), 1993, 201-206


1994

[3] M. A. Bennett, An ideal Waring problem with restricted summands, Acta Arith., LXVI.2 (1994), 125-132


1995

[4] M. A. Bennett, Simultaneous approximation to pairs of algebraic numbers, Canadian Mathematical Society Proceedings, Volume 15 (1995), 55-65 (pdf)


1996

[5] M. A. Bennett, Simultaneous rational approximation to binomial functions, Trans. Amer. Math. Soc. 348 (1996), 1717-1738 (pdf)

[6] M. A. Bennett, Solving norm form equations via lattice basis reduction, Rocky Mountain Journal of Mathematics 26 (1996), 815-837 (pdf)


1997

[7] M. A. Bennett, Effective measures of irrationality for certain algebraic numbers, J. Austral. Math. Soc. 62 (1997), 329-344 (pdf)

[8] M. A. Bennett, Explicit lower bounds for rational approximation to algebraic numbers, Proc. London Math. Soc. 75 (1997), 63-78 (pdf)

[9] M. A. Bennett, Solving families of simultaneous Pell equations, J. Number Th. 67 (1997), 246-251 (pdf)


1998

[10] M. A. Bennett and B. M. M. de Weger, On the Diophantine equation $|ax^{n}-by^{n}|=1$, Math. Comp. 67 (1998), 413-438 (pdf)

[11] M. A. Bennett, N. P. Dummigan and T. D. Wooley, The representation of integers by binary additive forms, Compositio Math. 111 (1998), 15-33 (pdf)

[12] M. A. Bennett, On the number of solutions of simultaneous Pell equations, J. Reine Angew. Math. 498 (1998), 173-200 (pdf)


1999

[13] M. A. Bennett and P. G. Walsh, The Diophantine equation $b^2X^4-dY^2=1$, Proc. Amer. Math. Soc. 127 (1999), 3481-3491 (pdf)

[14] M. A. Bennett, On consecutive integers of the form $ax^2, by^2$ and $cz^2$, Acta Arith. 88 (1999), 363-370 (pdf)


2000

[15] M. A. Bennett and P. G. Walsh, Simultaneous quadratic equations with few or no solutions, Indag. Mathem. 11 (2000), 1-12 (pdf)


2001

[16] M. A. Bennett, Rational approximation to algebraic numbers of small height : the Diophantine equation $|ax^n-by^n|=1$}, J. Reine Angew. Math. 535 (2001), 1-49 (pdf)

[17] M. A. Bennett, On the representation of unity by binary cubic forms, Trans. Amer. Math. Soc. 353 (2001), 1507-1534 (pdf)

[18] M. A. Bennett, On some exponential equations of S.S. Pillai, Canad. J. Math. 53 (2001), 897-922 (pdf)


2002

[19] M. Bauer and M. A. Bennett, Applications of the hypergeometric method to the generalized Ramanujan-Nagell equation, Ramanujan J. 6 (2002), 209-270 (pdf)

[20] M. A. Bennett, Lucas' square pyramid problem revisited, Acta Arith. 105 (2002), 341-347. (pdf)


2003

[21] M. A. Bennett, Pillai's conjecture revisited, J. Number Theory 98 (2003), 228-235. (pdf)

[22] M. A. Bennett, Recipes for ternary Diophantine equations of signature $(p,p,k)$, Proc. RIMS Kokyuroku (Kyoto) 1319 (2003), 51-55. (pdf)


2004

[23] M. A. Bennett and C. Skinner, Ternary Diophantine equations via Galois representations and modular forms, Canad. J. Math. 56 (2004), 23-54. (pdf)

[24] M. A. Bennett and B. Reznick, Positive rational solutions to $x^y=y^{mx}$ : a number-theoretic excursion, Amer. Math. Monthly 111 (2004), 13-21. (pdf)

[25] M. A. Bennett, V. Vatsal and S. Yazdani, Ternary Diophantine equations of signature $(p,p,3)$, Compositio Math. 140 (2004), 1399-1416. (pdf)

Click Transcript of Computations here to see details of the computations described in this paper.

[26] M. A. Bennett, Products of consecutive integers, Bull. London Math. Soc. 36 (2004), 683-694. (pdf)

[27] M. A. Bennett, K. Gyory and A. Pinter, On the Diophantine equation $1^k + 2^k + \cdots + x^k = y^n$, Compositio Math. 140 (2004), 1417-1431. (pdf)

[28] M. A. Bennett, On a theorem of Tartakowsky, Publ. Math. Debrecen 65 (2004), 269-279. (pdf)


2005

[29] M. A. Bennett, Powers in recurrence sequences : Pell equations, Trans. Amer. Math. Soc. 357 (2005), 1675-1691. (pdf)

[30] M. A. Bennett and P. Ingram, Torsion subgroups of elliptic curves in short Weierstrass form, Trans. Amer. Math. Soc. 357 (2005), 3325-3337. (pdf)

[31] M. A. Bennett, A question of Sierpinski on triangular numbers. Integers 5 (2005), no. 1, A25, 2 pp. (electronic). (pdf)


2006

[32] M. A. Bennett, N. Bruin, K. Gyory and L. Hajdu, Powers from products of consecutive terms in arithmetic progression. Proc. London Math. Soc. (3) 92 (2006), no. 2, 273--306. (pdf)

[33] M. A. Bennett, M. Cipu, M. Mignotte and R. Okazaki, On the number of solutions of simultaneous Pell equations. II. Acta Arith. 122 (2006), no. 4, 407--417. (pdf)

[34] M.A. Bennett, A. Togbe and P.G. Walsh, A generalization of a theorem of Bumby on quartic Diophantine equations. Int. J. Number Theory 2 (2006), no. 2, 195--206. (pdf)

[35] M. A. Bennett and J. Mulholland, On the Diophantine equation $x\sp n+y\sp n=2\sp \alpha pz\sp 2$. C. R. Math. Acad. Sci. Soc. R. Can. 28 (2006), no. 1, 6--11. (pdf)

[36] M. A. Bennett, K. Gyory, M. Mignotte and A. Pinter, Binomial Thue equations and polynomial powers. Compos. Math. 142 (2006), no. 5, 1103--1121. (pdf)

[37] M. A. Bennett, The equation $x^{2n}+y^{2n}=z^5$. J. Th. Nombres Bordeaux 18 (2006), 315-321. (pdf)


2007

[38] M. A. Bennett, The Diophantine equation $(x^k-1)(y^k-1)=(z^k-1)^t$. Indag. Math. 18 (2007), 1-19. (pdf)

[39] M. A. Bennett, Powers from five terms in arithmetic progression. Shorey conference proceedings, 2007, 1-6. (pdf)


2008

[40] M. A. Bennett, Differences between perfect powers. Canad. Math. Bull. 51 (2008), 337-347. (pdf)

[41] M. A. Bennett, Irrationality via the hypergeometric method, Diophantine Analysis and Related Fields -- DARF 2007/2008, 7-18, AIS CP 976, 200. (pdf)

[42] M. Bauer and M. A. Bennett, On a question of Erdos and Graham. L'Enseignement Math. 53 (2008), 259-264. (pdf)

[43] M. Bauer and M. A. Bennett, Prime factors of consecutive integers, Math. Comp. 77 (2008), 2455-2459. (pdf)

[44] M. A. Bennett, M. Filaseta and O. Trifonov, Yet another generalization of the Ramanujan-Nagell equation, Acta Arith. 134 (2008), 211-217. (pdf)


2009

[45] M. A. Bennett, M. Filaseta and O. Trifonov, On the factorization of consecutive integers. J. Reine Angew. Math. 629 (2009), 171-200. (pdf)


2010

[46] M. A. Bennett, J. Ellenberg and N. Ng, The Diophantine equation $A^4 + 2^\delta B^2 = C^p$. Inter. J. Number Theory 6 (2010), 1-27. (pdf)


2011

[47] M. A. Bennett, F. Luca and J. Mulholland, Twisted extensions of the cubic case of Fermat's Last Theorem. Ann. Sci. Math. Quebec. 35 (2011), 1-15. (pdf)


Accepted for publication

[48] M. A. Bennett and I. Chen, Multi-Frey $Q$-curves and the Diophantine equation $a^2 + b^6 = c^n$, to appear in Algebra and Number Theory, 24pp. (pdf)

[49] M. A. Bennett, A superelliptic equation involving alternating sums of powers, to appear in Publ. Math. Debrecen, 6pp. (pdf)

[50] M. A. Bennett and S. Yazdani, A local version of Szpiro's conjecture, to appear in Experimental Math., 19pp. (pdf)

[51] M. A. Bennett and R. Van Luijk, Squares from blocks of consecutive integers : a problem of Erdos and Graham, to appear in Indagationes Math., 6pp. (pdf)

[52] M. A. Bennett, Y. Bugeaud and M. Mignotte, Perfect powers with few binary digits and related Diophantine problems, to appear in Annali della Scuola Normale Superiore di Pisa, 13pp. (pdf)

[53] M. A. Bennett and S. Dahmen, Klein forms and the generalized superelliptic equation, to appear in Annals of Math., 57pp. (pdf)


Preprints

[54] M. A. Bennett, Perfect powers with few ternary digits, submitted for publication, 7pp (pdf)

[55] M. A. Bennett and Y. Bugeaud, Effective results for restricted rational approximation to quadratic numbers, submitted for publication, 10pp (pdf)

[56] M. A. Bennett, Y. Bugeaud and M. Mignotte, Perfect powers with few binary digits and related Diophantine problems II, submitted for publication, 20pp. (pdf)