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- W2247341403 abstract "Let $a,b,c$ be relatively prime positive integers such that $a^{2}+b^{2}=c^{2}.$ In 1956, Je'{s}manowicz conjectured that for any positive integer $n$, the only solution of $(an)^{x}+(bn)^{y}=(cn)^{z}$ in positive integers is $(x,y,z)=(2,2,2)$. Let $kgeq 1$ be an integer and $F_k=2^{2^k}+1$ be a Fermat number. In this paper, we show that Je'{s}manowicz' conjecture is true for Pythagorean triples $(a,b,c)=(F_k-2,2^{2^{k-1}+1},F_k)$." @default.
- W2247341403 created "2016-06-24" @default.
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- W2247341403 date "2013-04-01" @default.
- W2247341403 modified "2023-10-17" @default.
- W2247341403 title "Je'{s}manowicz' conjecture and Fermat numbers" @default.
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- W2247341403 doi "https://doi.org/10.48550/arxiv.1304.0514" @default.
- W2247341403 hasPublicationYear "2013" @default.
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