Browsing by Author "Pink, István"

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    On the Diophantine equation (x+1)(k) + (x+2)(k) + ... + (2x)(k) = y(n)
    (Elsevier, 2017-07-12) Bérczes, Attila; Pink, István; Savaş, Gamze; Soydan, Gökhan; Uludağ Üniversitesi/Fen-Edebiyet Fakültesi/Matematik Bölümü.; FWV-5620-2022; GEK-9891-2022; 57206274023; 23566953200
    In this work, we give upper bounds for n on the title equation. Our results depend on assertions describing the precise exponents of 2 and 3 appearing in the prime factorization of T-k(x) = (x + 1)(k) + (x + 2)(k) + ... + (2x)(k). Further, on combining Baker's method with the explicit solution of polynomial exponential congruences (see e.g. [6]), we show that for 2 <= x <= 13, k >= 1,y >= 2 and n >= 3 the title equation has no solutions.