The diophantine equation x2 = 4qn - 4q + 1

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Abstract

In this paper all integral solutions to the equation x2 = 4qn-4q+1 when q is an odd prime are determined. This is done by working in a quadratic field, using the unique factorization of ideals to reduce the problem to one about certain binary linear recurrences. One of the results is that the equation has no solutions with n > 2 if q > 5.

Original languageEnglish (US)
Pages (from-to)303-309
Number of pages7
JournalPacific Journal of Mathematics
Volume139
Issue number2
DOIs
StatePublished - Oct 1989

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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