Some observations on the diophantine equation $y^2=x!+A$ and related results

Authors

  • Maciej Ulas Jagiellonian University

Keywords:

Factorial function, Brocard-Ramanujan type equation, diophantine equation

Abstract

We consider the Brocard-Ramanujan type diophantine equation $y^2=x!+A$ and ask about values of $A\in\Z$ for which there is at least three solutions in positive integers. In particular we prove that the set $\cal{A}$ consisting integers with this property is infinite. In fact we construct two parametric family of integers contained in $\cal{A}$. We also give some computational results related to this equation. 10.1017/S0004972712000512

Published

2012-10-22

Issue

Vol. 86 No. 3 (2012)

Section

Articles
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