On arithmetic progressions on Pellian equations |
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| Authors: | A Dujella A Peth? P Tadi? |
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| Institution: | 1. Department of Mathematics, University of Zagreb, Bijeni?ka cesta 30, 10000, Zagreb, Croatia
2. Faculty of Informatics, University of Debrecen, H-4010, Debrecen, P.O. Box 12, Hungary
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| Abstract: | We consider arithmetic progressions consisting of integers which are y-components of solutions of an equation of the form x 2 ? dy 2 = m. We show that for almost all four-term arithmetic progressions such an equation exists. We construct a seven-term arithmetic progression with the given property, and also several five-term arithmetic progressions which satisfy two different equations of the given form. These results are obtained by studying the properties of a parametric family of elliptic curves. |
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