Triangular Numbers and Elliptic Curves

Jasbir S. Chahal, Jaap Top

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    Abstract

    Some arithmetic of elliptic curves and theory of elliptic surfaces is used to find all rational solutions (r, s, t) in the function field Q(m, n) of the pair of equations r(r + 1)/2 = ms(s + 1)/2 r(r + 1)/2 = nt(t + 1)/2. It turns out that infinitely many solutions exist. Several examples will be given.
    Original languageEnglish
    Pages (from-to)937-949
    Number of pages13
    JournalRocky mountain journal of mathematics
    Volume26
    Publication statusPublished - 1996

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