Pell Equations: Non-Principal Lagrange Criteria and Central Norms
نویسندگان
چکیده
We provide a criterion for the central norm to be any value in the simple continued fraction expansion of √ D for any non-square integer D > 1. We also provide a simple criterion for the solvability of the Pell equation x2 − Dy2 = −1 in terms of congruence conditions modulo D.
منابع مشابه
Lagrange, central norms, and quadratic Diophantine equations
As is often the case, some results get rediscovered over time. In particular, some rather striking results of Lagrange are often recreated. For instance, in [6], a result pertaining to the Pell equation for a prime discriminant was recast in the light of nonabelian cohomology groups. Yet, in [1], the authors acknowledged the fact that the result “has been discovered before,” and provided an ele...
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تاریخ انتشار 2012