Quadratic diophantine equations with parameters
نویسندگان
چکیده
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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We present infinite classes of quadratic Diophantine equations of the form px2 − cy2 = ±1, p any prime and c a positive integer, for which there are no solutions (x, y), yet for which there are solutions modulo n for all n ≥ 1. This generalizes earlier work where only the case p = 2 was considered. Mathematics Subject Classification: Primary: 11D09, 11R11, 11A55. Secondary: 11R29
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1980
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-37-1-133-141