WALAILAK JOURNAL OF SCIENCE AND TECHNOLOGY

Volume 16, No. 09, Month SEPTEMBER, Year 2019, Pages 647 - 653

On the diophantine equation 3x + p5y = z2

Kittipong LAIPAPORN, Saeree WANANIYAKUL, Prathomjit KHACHORNCHAROENKUL

Abstract Download PDF

In this paper, we present new series of solutions of the Diophantine equation 3x + p5y = z2 where p is a prime number and x; y and z are nonnegative integers using elementary techniques. Moreover, the equation has no solution if p is equivalent to 5 or 7 modulo 24.

Keywords

Exponential Diophantine equation, Catalan’s conjecture

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