14 Apr
2018
14 Apr
'18
6:41 a.m.
There exists an algorithm for finding integers m,n such that x = m^2 + n^2 , in amortised time proportional to (log x)^3 , where x is prime with x mod 4 = 1 . See Richard E. Crandall, Carl Pomerance "Prime Numbers: A Computational Perspective" Springer (2001), sect 2.3.2 pp 93--96 . Is there an analogous efficient algorithm for x = m^2 + m n + n^2 ? See https://en.wikipedia.org/wiki/Eisenstein_integer https://oeis.org/A034017 , https://oeis.org/A000086 What about more general binary quadratic forms? Fred Lunnon