On the Diophantine equation $1^k+2^k+dotsb+x^k=y^n$

[摘要] In this paper, we resolve a conjecture of Schäffer on the solvability of Diophantine equations of the shape $1^k + 2^k + dotsb + x^k = y^n$, for $1 leq k leq 11$. Our method, which may, with a modicum of effort, be extended to higher values of k, combines a wide variety of techniques, classical and modern, in Diophantine analysis.

[学科分类] 数学（综合）