Abstract

In this short mathematical letter, we introduce an interesting result about the powers of a general form of Diophantine equations. This work gives a condition that makes this Diophantine equation have no possible natural numbers as a solution or have specific prime numbers as a solution. The investigation in this short article uses the Fermat-Euler theorem and the steps of the proof are short and easy. Some applications are also introduced in this short article in order to prove the usefulness of the results. We hope that the result is useful for researchers of all scientific fields.