On a Diophantine problem of Bennett

On a Linear Diophantine Problem of Frobenius

Let a1, a2, . . . , ak be positive and pairwise coprime integers with product P . For each i, 1 ≤ i ≤ k, set Ai = P/ai. We find closed form expressions for the functions g(A1, A2, . . . , Ak) and n(A1, A2, . . . , Ak) that denote the largest (respectively, the number of) N such that the equation A1x1 + A2x2 + · · · + Akxk = N has no solution in nonnegative integers xi. This is a special case of...

A Diophantine Problem on Elliptic Curves

This paper examines simultaneous diophantine approximations to coordinates of certain points on a product of elliptic curves. Specifically, let p(z) be a Weierstrass elliptic function with algebraic invariants and complex multiplication. Suppose that 0 is cubic over the "field of multiplications" of p(z) and that u 6 C such that f = (p{u), p(/3u), p(/32u)) is defined. We study approximations to...

An Interesting Diophantine Problem on Triples-I

We search for three non-zero distinct integers a, b, c such that, if a non-zero integer is added to the sum of any pair of them as well as to their sum, the results are all squares. Index Terms – Diophantine Problem, Integer Triple, System of Equations.

The Diophantine Frobenius Problem

A Diophantine System and a Problem on Cubic Fields

We give a complete solution to a system of Diophantine equations related to a problem on the fundamental unit of a family of cubic fields.