Diophantine m-tuples for linear polynomials II. Equal degrees |
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Authors: | Andrej Dujella Clemens Fuchs Gary Walsh |
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Affiliation: | a Department of Mathematics, University of Zagreb, Bijeni?ka cesta 30, 10000 Zagreb, Croatia b Institut für Mathematik, Technische Universität Graz, Steyrergasse 30/II, 8010 Graz, Austria c Department of Mathematics, University of Ottawa, 585 King Edward St., Ottawa, Ontario, K1N 6N5, Canada |
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Abstract: | In this paper we prove the best possible upper bounds for the number of elements in a set of polynomials with integer coefficients all having the same degree, such that the product of any two of them plus a linear polynomial is a square of a polynomial with integer coefficients. Moreover, we prove that there does not exist a set of more than 12 polynomials with integer coefficients and with the property from above. This significantly improves a recent result of the first two authors with Tichy [A. Dujella, C. Fuchs, R.F. Tichy, Diophantine m-tuples for linear polynomials, Period. Math. Hungar. 45 (2002) 21-33]. |
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Keywords: | 11D09 11C08 |
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