Proof of Qiu Lupeng Conjecture(Part 1)

Abstract

This paper studies the Qiu Lupeng Conjecture (Beautiful Equalities Conjecture).We discuss a Diophantine equation with infinitely many terms on the left-hand side.Using modular arithmetic modulo 2, modulo 3 and modulo 5, we analyze parity and remainder conditions for integer solutions.The result shows the equation only has three groups of integer solutions.This is Part 1 of the proof.