For integer n > 2, x1^(n + 1) + x2^(n + 1) + ... + xn^(n + 1) = z^(n + 1), where z and x1 through xn are integers, has no positive integer solutions {Euler conjecture}. Case x1^4 + x2^4 + x3^4 = z^4 (n + 1 = 4) is false. Case x1^5 + x2^5 + x3^5 + x4^5 = z^5 (n + 1 = 5) is false. Fermat's last theorem is case x1^3 + x2^3 = z^3, where n = 2 (n + 1 = 3), which is true.
Mathematical Sciences>Number Theory>Theorem
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Date Modified: 2022.0224