Enumerating solutions to p(a)+q(b)=r(c)+s(d)

D.J. Bernstein

    Research output: Contribution to journalArticleAcademicpeer-review

    14 Citations (Scopus)

    Abstract

    Let p; q; r; s be polynomials with integer coefficients. This paper presents a fast method, using very little temporary storage, to find all small integers (a; b; c; d) satisfying p(a)+q(b) = r(c)+s(d). Numerical results include all small solutions to a4+b4+c4 = d4; all small solutions to a4+b4 = c4+d4; and the smallest positive integer that can be written in 5 ways as a sum of two coprime cubes.
    Original languageEnglish
    Pages (from-to)389-394
    JournalMathematics of Computation
    Volume70
    DOIs
    Publication statusPublished - 2001

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