TY - JOUR
T1 - A deterministic algorithm for solving n = fu2+gv2in coprime integers u and v
AU - Hardy, Kenneth
AU - Muskat, Joseph B.
AU - Williams, Kenneth S.
PY - 1990/7
Y1 - 1990/7
N2 - We give a deterministic algorithm for finding all primitive representations of a natural number n in the form fu2+gv2where 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 ≥ (n1 4(logn)3(loglogn)(logloglogn)), uniformly in and g.
AB - We give a deterministic algorithm for finding all primitive representations of a natural number n in the form fu2+gv2where 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 ≥ (n1 4(logn)3(loglogn)(logloglogn)), uniformly in and g.
UR - http://www.scopus.com/inward/record.url?scp=84966251650&partnerID=8YFLogxK
U2 - 10.1090/S0025-5718-1990-1023762-3
DO - 10.1090/S0025-5718-1990-1023762-3
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AN - SCOPUS:84966251650
SN - 0025-5718
VL - 55
SP - 327
EP - 343
JO - Mathematics of Computation
JF - Mathematics of Computation
IS - 191
ER -