Bérczes, AttilaPink, István2023-09-242023-09-242017-07-12Berczes, A. vd. (2018). ''On the Diophantine equation (x+1)(k) + (x+2)(k) + ... + (2x)(k) = y(n)''. Journal of Number Theory, 183, 326-351.0022-314X1096-1658https://doi.org/10.1016/j.jnt.2017.07.020https://www.sciencedirect.com/science/article/pii/S0022314X17302895http://hdl.handle.net/11452/33996In 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.eninfo:eu-repo/semantics/openAccessMathematicsPower sumsPowersPolynomial-exponential congruencesLinear forms in two logarithmsSumsArticle0004143802000162-s2.0-85029553067326351183MathematicsDiophantine Equation; Number; Linear Forms in Logarithms