Abstract
In 2014, T. Komatsu and L. Szalay studied the balancing binomial coefficients. In this paper, we focus on the following Diophantine equation \begin{equation*} \binom{1}{5}+\binom{2}{5}+…+\binom{x-1}{5}=\binom{x+1}{5}+…+\binom{y}{5} \end{equation*} where $y>x>5$ are integer unknowns. We prove that the only integral solution is $(x,y)=(14,15)$. Our method is mainly based on the linear form in elliptic logarithms.
Citation
Shane Chern. "A note on balancing binomial coefficients." Proc. Japan Acad. Ser. A Math. Sci. 91 (8) 110 - 111, October 2015. https://doi.org/10.3792/pjaa.91.110
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