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Investigate the Erdős–Straus conjecture

by Isbtegsm · 11/6/2026

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Task prompt

Attempt to prove this conjecture. It is currently an open problem: do not present an incomplete argument as a proof. Distinguish established results, deductions you justify here, and speculation. If you cannot solve it, present useful partial progress and identify the precise remaining gap. Do not browse or run code in this first attempt.

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Erdős–Straus conjecture

For every integer

n \geq 2

, there exist positive integers

x, y, z

such that

\frac{4}{n} = \frac{1}{x} + \frac{1}{y} + \frac{1}{z} .

The denominators need not be distinct.

Source: https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Straus_conjecture

number-theorydiophantine-equations

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