Lagrange's Algorithm Revisited: Solving at2 + btu + cu2 = n in the Case of
Keith R. Matthews
School of Mathematics and Physics
University of Queensland
Brisbane, QLD 4072
Centre for Mathematics and its Applications
Australian National University
Canberra, ACT 0200
We make more accessible a neglected continued fraction algorithm of
Lagrange for solving the equation
at2 + btu + cu2 = n
prime integers t, u, where a > 0,
gcd(a,n) = 1, and D = b2 - 4ac
The cases D = -4 and D = -3 present a
consecutive convergents phenomenon which aids
the search for solutions.
Full version: pdf,
August 26 2014; revised version received September 22 2014.
Published in Journal of Integer Sequences, November 5 2014.
Journal of Integer Sequences home page