An Interesting Number Theoretic Problem

TL;DR

This paper extends a classic Olympiad problem by exploring a simple variant involving real constants and the equation a^k + b^k = c, providing a new mathematical insight.

Contribution

It introduces a novel extension of an Olympiad problem related to approximating the exponent k in the equation a^k + b^k = c with real constants.

Findings

Proves a new result extending the Olympiad problem

Provides insights into approximating the exponent k

Simplifies the understanding of the related number theoretic problem

Abstract

In this short note we prove a result that is an extension of an old Olympiad problem and is a very simple variant of the question of finding an approximation for $k$, where it is a nonzero constant and it satisfies the equation $a^k+b^k=c$, where $a,b,c$ are all real constants.