MathDB

2

Part of 2014 Irish Math Olympiad

Problems(1)

Prove divisibility by a given expression

Source: Irish Math Olympiad 2014 Q2

3/14/2017
Prove that for N>1N>1 that (N2)2014āˆ’(N11)106(N^{2})^{2014} - (N^{11})^{106} is divisible by N6+N3+1N^6 + N^3 +1
Is this just a proof by induction or is there a more elegant method? I don't think calculating N=2N = 2 was expected.
number theorynumber theory unsolvedDivisibilityinduction