Glasnik Matematicki, Vol. 41, No.1 (2006), 1-8.

COMPUTATIONAL EXPERIENCES ON NORM FORM EQUATIONS FORMING ARITHMETIC PROGRESSIONS

A. Bérczes and A. Pethö

Institute of Mathematics, University of Debrecen, Number Theory Research Group, Hungarian Academy of Sciences and University of Debrecen, H-4010 Debrecen, P.O. Box 12, Hungary
e-mail: berczesa@math.klte.hu

Faculty of Informatics, University of Debrecen, H-4010 Debrecen, P.O. Box 12, Hungary
e-mail: pethoe@inf.unideb.hu

Abstract.   In the present paper we solve the equation

NK/Q(x0 + x1α + x2α2 + ... + xn -1αn -1) = 1

in x0, ... , xn -1 in Z, such that x0, ... , xn -1 is an arithmetic progression, where α is a root of the polynomial xn - a, for all integers 2 ≤ a ≤ 100 and n ≥ 3.

2000 Mathematics Subject Classification.   11D57, 11D59, 11B25.

Key words and phrases.   Norm form equation, arithmetic progression, binomial Thue equation.

Full text (PDF) (free access)

DOI: 10.3336/gm.41.1.01

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