Equal sums of like polynomials

TD Browning

doi:10.1112/S0024609305004741

Equal sums of like polynomials

TD Browning

Research output: Contribution to journal › Article (Academic Journal) › peer-review

5 Citations (Scopus)

Abstract

Let f epsilon 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 >= 7. Also the corresponding situation is investigated for equal sums of three like polynomials.

Translated title of the contribution	Equal sums of like polynomials
Original language	English
Pages (from-to)	801 - 808
Number of pages	8
Journal	Bulletin of the London Mathematical Society
Volume	37 (6)
DOIs	https://doi.org/10.1112/S0024609305004741
Publication status	Published - Dec 2005

Bibliographical note

Publisher: Cambridge University Press
Other identifier: IDS Number: 998SJ

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http://www.journals.cambridge.org/action/displayFulltext?type=1&fid=358673&jid=BLM&volumeId=37&issueId=06&aid=358672

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title = "Equal sums of like polynomials",

abstract = "Let f epsilon 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 >= 7. Also the corresponding situation is investigated for equal sums of three like polynomials.",

author = "TD Browning",

note = "Publisher: Cambridge University Press Other identifier: IDS Number: 998SJ ",

year = "2005",

month = dec,

doi = "10.1112/S0024609305004741",

language = "English",

volume = "37 (6)",

pages = "801 -- 808",

journal = "Bulletin of the London Mathematical Society",

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T1 - Equal sums of like polynomials

AU - Browning, TD

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PY - 2005/12

Y1 - 2005/12

N2 - Let f epsilon 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 >= 7. Also the corresponding situation is investigated for equal sums of three like polynomials.

AB - Let f epsilon 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 >= 7. Also the corresponding situation is investigated for equal sums of three like polynomials.

U2 - 10.1112/S0024609305004741

DO - 10.1112/S0024609305004741

M3 - Article (Academic Journal)

SN - 1469-2120

VL - 37 (6)

SP - 801

EP - 808

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

ER -

Equal sums of like polynomials

Abstract

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