Is it possible to show that, given $n$, there are infinite values of $k$ giving solutions of the equation: $$x^n+ky^n=z^n$$ with $k,x,y,z,n$ natural numbers? The constrains are: $$2\lt n, 1\lt k$$
2026-04-13 21:15:58.1776114958
Solution of a Diophantine equation involving powers
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Hint: Let $x=y=2$, or more generally $x=y=a$. Find suitable values of $k$.