An effective p-adic analogue of a theorem of Thue
An effective p-adic analogue of a theorem of Thue II. The greatest prime factor of a binary form
An effective p-adic analogue of a theorem of Thue III. The diophantine equation
An effective Shafarevich theorem for elliptic curves
An elliptic curve having large integral points
The main purpose of this paper is to prove that the elliptic curve has only the integral points and , using elementary number theory methods and some known results on quadratic and quartic Diophantine equations.
An estimate for Frobenius' Diophantine problem in three dimensions.
An Estimate for the Fundamental Solutions of a Generalized Pell Equation.
An explicit upper bound for the number of solutions of the S-unit equation.
An explicit version of Birch's Theorem
An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma
An extension of a theorem of Euler
An extension of Sophie Germain's method to a wide class of diophantine equations.
An identity Ramanujan probably missed
"Ramanujan's 6-10-8 identity" inspired Hirschhorn to formulate his "3-7-5 identity". Now, we give a new "6-14-10 identity" which we suppose Ramanujan would have discovered but missed to mention in his notebooks.
An improved algorithm for the solution of integer programs by the solution of associated diophantine equations
An Improved Bound for Prime Solutions of Some Ternary Equations.
An improved upper bound for G(k) in Waring's problem for relatively small k
An improvement of the quantitative subspace theorem
An irregular D(4)-quadruple cannot be extended to a quintuple
An isoperimetric inequality for the area of plane regions defined by binary forms
An note on the Tarry-Escott problem.