On D so that x2 - Dy2 represents m and -m and not -1

Robertson, John P. (2009) On D so that x2 - Dy2 represents m and -m and not -1. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 25 (2). pp. 155-164. ISSN 0866-0174

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Abstract

For m = 25, 100, p, 2p, 4p, or 2p 2 , where p is prime, we show that there is at most one positive nonsquare integer D so that the form x2 − Dy2 primitively represents m and −m and does not represent −1. We give support for a conjecture that for any m > 1 not listed above, there are infinitely many D so that the form x 2 − Dy2 primitively represents m and −m and does not represent −1.

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