Lagrange's algorithm revisited: Solving at2 + btu + cu2 = n in the case of negative discriminant

Keith R. Matthews*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We make more accessible a neglected continued fraction algorithm of Lagrange for solving the equation at2 + btu + cu2 = n in relatively prime integers t, u, where a> 0, gcd(a,n) = 1, and D = b2 - 4ac < 0. The cases D = -4 and D = -3 present a consecutive convergents phenomenon which aids the search for solutions.

    Original languageEnglish
    Article number14.11.1
    JournalJournal of Integer Sequences
    Volume17
    Issue number11
    Publication statusPublished - 5 Nov 2014

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