In this paper, we show that the diophantine equation Fn = p ± p has only finitely many positive integer solutions (n, p, a, b), where p is a prime number and max{a, b} ≥ 2.

The Erdős–Moser equation is a Diophantine equation proposed more than 60 years ago which remains unresolved to this day. In this paper, we consider the problem in terms of divisibility of power sums and in terms of certain Egyptian fraction equations. As a consequence, we show that solutions must satisfy strong divisibility properties and a restrictive Egyptian fraction equation. Our studies le...

In this paper, we prove that there are infinitely many positive integers N such that the Diophantine equation (x2 + y)(x + y2) = N(x− y)3 has no nontrivial integer solution (x, y).

The complete solution in (n, yx, yj) 6 Z3 of the Diophantine equation b„ = ±2yi yi is given, where (bn)nez is Berstel's recurrence sequence defined by />o = Z>i=0, b2 = l, b„+3 = 2bn+2 4b„+l + 4bn.