A note on balancing binomial coefficients
Copyright policy )A note on balancing binomial coefficients
In 2014, T. Komatsu and L. Szalay studied the balancing binomial coefficients. In this paper, we focus on the following Diophantine equation $$\binom{1}{5}+\binom{2}{5}+...+\binom{x-1}{5}=\binom{x+1}{5}+...+\binom{y}{5}$$ 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.
Several minor corrections. Final version published in Proc. Japan Acad. Ser. A Math. Sci
- Zhejiang Ocean University China (People's Republic of)
linear form in elliptic logarithms, 11Y50, Mathematics - Number Theory, FOS: Mathematics, 11D25, 11G05, 11Y50, binomial coefficient, 11D25, Number Theory (math.NT), 11G05, Balancing problem
linear form in elliptic logarithms, 11Y50, Mathematics - Number Theory, FOS: Mathematics, 11D25, 11G05, 11Y50, binomial coefficient, 11D25, Number Theory (math.NT), 11G05, Balancing problem
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!