On D so that x2 − Dy2 = ±m

Robertson, John P. (2006) On D so that x2 − Dy2 = ±m. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 22 (2). pp. 143-148. ISSN 0866-0174

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Abstract

We prove that for any integer m 6 = 0, ±2, there are infinitely many positive integers D for which the form x2 −Dy2 primitively represents m, −m, and −1. We do this by constructing an infinite sequence of such D’s associated with each m. Also, when m is odd, we relate the existence of additional such D’s to well-known conjectures.

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