EQUAL SUMS OF LIKE POLYNOMIALS

DOI10.1112/S0024609305004741zbMATH Open1099.11011arXivmath/0507541MaRDI QIDQ3375322

T. D. Browning

Publication date: 8 March 2006

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/math/0507541

zbMATH Keywords

cubic Diophantine equationcounting solutionsnon-trivial solutionsequal sums

Mathematics Subject Classification ID

Waring's problem and variants (11P05) Counting solutions of Diophantine equations (11D45) Cubic and quartic Diophantine equations (11D25)

Related Items (2)

On the asymmetric additive energy of polynomials ⋮ On some matrix counting problems

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