Volker Ziegler
Published 2021-03-26Version 1
Let us denote by $F_n$ the $n$-th Fibonacci number. In this paper we show that for a fixed integer $y$ there exists at most one integer exponent $a>0$ such that the Diophantine equation $F_n+F_m=y^a$ has a solution $(n,m,a)$ in positive integers satisfying $n>m>0$, unless $y=2,3,4,6$ or $10$.
Perfect powers in alternating sum of consecutive cubes
On the Diophantine equation $(x+1)^{k}+(x+2)^{k}+...+(2x)^{k}=y^n$
On the Diophantine equation $f(x)=2f(y)$
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