On the Diophantine Equation 71^x-73^y=z^3.

Saowaros Srisook, Apisit Pakapongpun, Natdanai Chailangka

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Source: Crossref

Published: Jan 1, 2026

DOI: 10.69793/ijmcs/04.2026/spc

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Source abstract

In this paper, we study the exponential Diophantine equation 71^x-73^y=z^3, where x,y,z are non-negative integers. Using a cubic residue criterion together with a quadratic congruence modulo 73, we prove that the equation has the unique solution (x,y,z)=(0,0,0).

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