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Let a, b be integers, and let P(x) = ax^3+bx. For any positive integer n we say that the pair (a,b) is n-good if n | P(m)-P(k) implies n | m - k for all integers m, k. We say that (a,b) is very \ good if (a,b) is n-good for infinitely many positive integers n.
(a) Find a pair (a,b) which is 51-good, but not very good.(b) Show that all 2010-good pairs are very good.
Proposed by Okan Tekman, Turkey

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