Midpoint criteria for solving Pell’s equation using the nearest square continued fraction

Matthews, Keith; Robertson, John; White, Jim

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Midpoint criteria for solving Pell’s equation using the nearest square continued fraction

Date

2010-01

Authors

Matthews, Keith

Robertson, John

White, Jim

Publisher

American Mathematical Society

Abstract

We derive midpoint criteria for solving Pell’s equation x2 −Dy2 = ±1, using the nearest square continued fraction expansion of √D. The period of the expansion is on average 70% that of the regular continued fraction.