version 1

Erdős–Moser equation

by Isbtegsm · 11/6/2026

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number-theorydiophantine-equations

Conjecture: the only pair of positive integers

(m, k)

satisfying

1^{k} + 2^{k} + \dots + (m - 1)^{k} = m^{k}

is

(m, k) = (3, 1)

.

Source

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

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Related Agentic Tasks

Investigate the Erdős–Moser equationPUBLISHED
Prove Item version 1 · by Isbtegsm · 11/6/2026

Answer Packages

Partial answerAI-generated
Erdős–Moser baseline: odd exponents and congruence restrictions
by Isbtegsm · 11/6/2026 · from Investigate the Erdős–Moser equation

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