Let a, b, c and n be positive integers such that an is divisible by b, such that bn is divisible by c, and such that cn is divisible by a.
Prove that \left(a \plus{} b \plus{} c\right)^{n^2 \plus{} n \plus{} 1} is divisible by abc.
An even broader generalization, though not part of the QEDMO problem and not quite number theory either:
If u and n are positive integers, and a1, a2, ..., au are integers such that ain is divisible by a_{i \plus{} 1} for every i such that 1≤i≤u (we set a_{u \plus{} 1} \equal{} a_1 here), then show that \left(a_1 \plus{} a_2 \plus{} ... \plus{} a_u\right)^{n^{u \minus{} 1} \plus{} n^{u \minus{} 2} \plus{} ... \plus{} n \plus{} 1} is divisible by a1a2...au. number theorynumber theory proposed