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Equal Sums of Like Polynomials
Author(s) -
Browning T. D.
Publication year - 2005
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609305004741
Subject(s) - mathematics , degree (music) , integer (computer science) , polynomial , mathematics subject classification , combinatorics , discrete mathematics , pure mathematics , mathematical analysis , physics , computer science , acoustics , programming language
Let f ∈ 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. 2000 Mathematics Subject Classification 11D45, 11P05.