Square classes of generalized Pell sequences

doi:10.3969/j.issn.1008-0171.2003.02.002

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DOI: 10.3969/j.issn.1008-0171.2003.02.002

Square classes of generalized Pell sequences

Abstract：Let t be a positive integer with t>1, and let U={Uk}k=0 be the generalized Pell sequence with parametes t.In this paper, we prove that if t=2dr2 and(t+t2+1)d+(t-t2+1)d=4s2,where d, r, s are positive integers satisfying 2d and d is square free,then U has exactly one square class {Ud,U2d}.Otherwise, U has no square classes.

Keywords：generalized Pell sequencesquare classDiophantine equation

Publication Date：2003-01-01

Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)

Pages：5( 6-10 )

JOURNAL OF FOSHAN UNIVERSITY(NATURAL SCIENCE EDITION)

ISSN：1008-0171

Year, Vol.(Issue)：2003,21(2)