In this paper we consider the problem of characterizing those perfect squares that can be expressed as the sum of consecutive squares where the initial term in this sum is the square of k. This problem is intimately related to that of finding all integral points on elliptic curves belonging to a...

The Elliptic Logarithm Method has been applied with great success to the problem of computing all integer solutions of equations of degree 3 and 4 defining elliptic curves. We extend this method to include any equation f(u,v)=0 that defines a curve of genus 1. Here f is a polynomial with integer...

The Elliptic Logarithm Method has been applied with great success to the problem of computing all integer solutions of equations of degree 3 and 4 defining elliptic curves. We extend this method to include any equation f(u,v)=0 that defines a curve of genus 1. Here f is a polynomial with integer...

We solve a problem posed recently by J.H.E. Cohn, in proving that x = y = 1 is the only solution in nonnegative integers to the diophantine equation x^2 - 3 y^4 = -2.

A Q-derived polynomial is a univariate polynomial, defined over the rationals, with the property that its zeros, and those of all its derivatives are rational numbers. There is a conjecture that says that Q-derived polynomials of degree 4 with distinct roots for themselves and all their...

A Q-derived polynomial is a univariate polynomial, defined over the rationals, with the property that its zeros, and those of all its derivatives are rational numbers. There is a conjecture that says that Q-derived polynomials of degree 4 with distinct roots for themselves and all their...