Lagrange ’ s Algorithm Revisited : Solving at 2 + btu + cu 2 = n in the Case of Negative Discriminant Keith
نویسنده
چکیده
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.
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