Lagrange's Algorithm Revisited: Solving at 2 + btu + cu 2 = n in the Case of Negative Discriminant

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 consec Show more