Question 178
Let $u$ be a nonzero natural number.
Prove that there are only finitely many triples of natural numbers $(a, b, n)$ such that $n! = u^{a} - u^{b}$.
Note: recall that $0! = 1! = 1$.
Prove that there are only finitely many triples of natural numbers $(a, b, n)$ such that $n! = u^{a} - u^{b}$.
Note: recall that $0! = 1! = 1$.