Question

a nice problem for u

Answer 1

find all positive integers like n such that
\[\frac{n^3+1}{n-1}\]
is a positive integer too

Answer 2

\[\frac{n^3+1}{n-1}=\frac{n^3-1+2}{n-1}=\frac{(n-1)(n^2+n+1)+2}{n-1}=n^2+n+1+\frac{2}{n-1}\]

Answer 3

so positive solutions would be for:
n - 1 = 1 => n = 2
n - 1 = 2 => n = 3