A note on the number of solutions of the generalized Ramanujan-Nagell equation
A note on the number of solutions of the generalized Ramanujan-Nagell equation
Let be a positive integer, and let be an odd prime with . In this paper we use a result on the rational approximation of quadratic irrationals due to M. Bauer, M. A. Bennett: Applications of the hypergeometric method to the generalized Ramanujan-Nagell equation. Ramanujan J. 6 (2002), 209–270, give a better upper bound for , and also prove that if the equation has integer solutions , the least solution of the equation satisfies , and , where is an effectively computable constant...
A Note on Thue's Equation Over Function Fields.
A note on Waring's problem in GF (p)
A note on Waring's problem in p-adic fields
A numerical bound for small prime solutions of some ternary linear equations
A parametric family of elliptic curves
A parametric family of quartic Thue equations
A parametric family of sextic Thue equations
A parametrization of equilateral triangles having integer coordinates.
A partition problem of Frobenius, II
A propos du problème de Waring
A Quadratic Diophantine Equation.
A quantitative lower bound for the greatest prime factor of (ab+1)(bc+1)(ca+1)
A quantitative version of Runge's theorem on diophantine equations
A quantitative version of Siegel's theorem: integral points on elliptic curves and Catalan curves.
A question of Sierpinski on triangular numbers.
A rationality condition for the existence of odd perfect numbers.
A Reciprocity Formula for Quadratic Forms.
A remark on a Diophantine equation of S. S. Pillai
S. S. Pillai proved that for a fixed positive integer , the exponential Diophantine equation , , has only finitely many solutions in integers and . We prove that when is of the form , the above equation has no solution in integers and with .