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  • 1 University of Zagreb Department of Mathematics Bijenička cesta 30 10000 Zagreb Croatia
  • 2 University of Debrecen Faculty of Informatics 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 x2dy2 = 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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