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

Chris Skinner

doi:10.2140/pjm.1989.139.303

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

Chris Skinner

Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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 language	English (US)
Pages (from-to)	303-309
Number of pages	7
Journal	Pacific Journal of Mathematics
Volume	139
Issue number	2
DOIs	https://doi.org/10.2140/pjm.1989.139.303
State	Published - Oct 1989

All Science Journal Classification (ASJC) codes

General Mathematics

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10.2140/pjm.1989.139.303

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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.",

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AB - 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.

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

Abstract

All Science Journal Classification (ASJC) codes

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