The Diophantine equation $f(x)=g(y)$
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- by Todd Cochrane PDF
- Proc. Amer. Math. Soc. 109 (1990), 573-577 Request permission
Abstract:
Let $f(x),g(y)$ be polynomials over $\mathbb {Z}$ of degrees $n$ and $m$ respectively and with leading coefficients ${a_n},{b_m}$. Suppose that $m|n$ and that ${a_n}/{b_m}$ is the $m$th power of a rational number. We give two elementary proofs that the equation $f(x) = g(y)$ has at most finitely many integral solutions unless $f(x) = g(h(x))$ for some polynomial $h(x)$ with rational coefficients taking integral values at infinitely many integers.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 573-577
- MSC: Primary 11D41
- DOI: https://doi.org/10.1090/S0002-9939-1990-1019271-X
- MathSciNet review: 1019271