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EQUAL SUMS OF LIKE POLYNOMIALS

Published online by Cambridge University Press:  12 December 2005

T. D. BROWNING
Affiliation:
School of Mathematics, Bristol University, Bristol BS8 1TW, United Kingdom, t.d.browning@bristol.ac.uk
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Abstract

Let $f \in \Z[x]$ be a polynomial of degree d. The paucity of non-trivial positive integer solutions to the equation $f(x_1)+f(x_2)=f(x_{3})+f(x_{4})$ is established, provided that $d \geq 7$. Also the corresponding situation is investigated for equal sums of three like polynomials.

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Copyright
© The London Mathematical Society 2005

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Footnotes

This work was undertaken while the author was at Oxford University, supported by EPSRC grant number GR/R93155/01.
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