A deterministic algorithm for solving n=fu^2+gv^2 in coprime integers u and v
Abstract
We give a deterministic algorithm for finding all primitive representations of a natural number n in the form f{u^2} + g{v^2} , where f and g are given positive coprime integers, and n ≥ f + g + 1 , (n,fg) = 1 . The running time of this algorithm is at most O({n^{1/4}}{(log n)^3}(log log n)(log log log n)), uniformly in f and g.
- Publication:
-
Mathematics of Computation
- Pub Date:
- July 1990
- DOI:
- 10.1090/S0025-5718-1990-1023762-3
- Bibcode:
- 1990MaCom..55..327H