A short proof of Erdös–Straus conjecture for every n ≡ 13 mod 24

Abstract

Rhe Erdös–Straus conjecture states that the equation has positive integer solutions x, y, z for every positive integers n ≥ 2. In this short note we find explicitly the solutions of the famous conjecture for the case n ≡ 13 mod 24.

Subject Classification: [2010]:

• 11D72
• 11D45
• 11P81

Keywords:

• Conjecture Erdös–Straus
• Diophantine equations