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Lander and Parkin: a counterexample in fifth powers

Contribution grade

Number theory · Scoped scientific or research-capability contribution

Reference score7,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

Found 27^5 + 84^5 + 110^5 + 133^5 = 144^5 by computer search, disproving Euler’s proposed lower bound on the number of like powers needed to sum to another.

Scientific scope

Found 27^5 + 84^5 + 110^5 + 133^5 = 144^5 by computer search, disproving Euler’s proposed lower bound on the number of like powers needed to sum to another. Scope limitation: The displayed identity is a finite exact witness. The historical search used a CDC 6600; it is not evidence of a modern AI-model contribution. The source’s minimality statement requires its search scope and is not established merely by checking the equality.

Evidence

Assessment uses the catalogue-linked source evidence for the stated contribution. The displayed identity is a finite exact witness. The historical search used a CDC 6600; it is not evidence of a modern AI-model contribution. The source’s minimality statement requires its search scope and is not established merely by checking the equality.

Contributors

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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