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Number Theory Open

Erdős–Straus Conjecture

For every integer n ≥ 2, do there exist positive integers x, y, z such that 4/n = 1/x + 1/y + 1/z? A statement about Egyptian fraction expansions of 4/n.

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  1. Validated increment

    Verified for all n up to an extended computational bound

    Machine search extended the range of n for which an explicit (x, y, z) solution is known, using modular case divisions standard in the literature.

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    Solutions archived through prior computational thresholds

    New certified

    Solutions certified through n ≤ 10^17 in the Arbiter corpus

    Arbiter computational number-theory cluster

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