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arXiv · 1912.12687

Je{\'s}manowicz' conjecture for polynomials

Jerome T. Dimabayao
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Abstract

Let $(a,b,c)$ be pairwise relatively prime integers such that $a^2 + b^2 = c^2$. In 1956, Je{\'s}manowicz conjectured that the only solution of $a^x + b^y = c^z$ in positive integers is $(x,y,z)=(2,2,2)$. In this note we prove a polynomial analogue of this conjecture.

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Jerome T. Dimabayao. 2019-12-29. Je{\'s}manowicz' conjecture for polynomials. https://doi.org/10.1007/s10998-020-00339-w

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