Fermat's Equation Has No Solution with Some Prime Components

2015/05/07 by Yu-Lin Chou, Chou, Yu-Lin
Mathematics · #11A99 #11D41 #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #History and Theory of Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1505.02457

openalex publication_date 2015/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Within the scope of elementary number theory, we prove that, as the main result, if 1 ≤ x < y < z are integers such that at least one of y, z, x+y is prime then xⁿ+yⁿ ≠ zⁿ for every odd integer n ≥ 3. This result covers a special case of a conjecture of Abel, and furnishes a definite way to construct infinitely many setwise coprime integers that do not satisfy the Fermat's equation uniformly in n.

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