Equal sums of like polynomials

2005/07/26 by T. D. Browning, Browning, T. D.
Mathematics · #11D45 (11P05) #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11D45

paper · pdf · doi:10.48550/arxiv.math/0507541

8 pages; to appear in Bull. London Math. Soc

arxiv created 2005/07/26 · arxiv updated 2009/12/01

Abstract

Let f be a polynomial of degree d>6, with integer coefficients. Then the paucity of non-trivial positive integer solutions to the equation f(a)+f(b)=f(c)+f(d) is established. The corresponding situation for equal sums of three like polynomials is also investigated.

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