Euler's sum of powers conjecture

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In number theory, Euler's conjecture is a disproved conjecture related to Fermat's Last Theorem. It was presented by Leonhard Euler in 1778 to the Academy of Sciences of St. Petersburg. It states that for all integers n and k greater than 1, if the sum of n many kth powers of positive integers is itself a kth power, then n is greater than or equal to k: a 1 k + a 2 k + ⋯ + a n k = b k ⟹ n ≥ k {\displaystyle a_{1}^{k}+a_{2}^{k}+\dots +a_{n}^{k}=b^{k}\implies n\geq k} The conjecture represents an attempt to generalize Fermat...

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