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India TST : Day4 :Problem 2

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May 22, 2009
number theory proposednumber theory

Problem Statement

Find all integers n≥2 n\ge 2 with the following property:
There exists three distinct primes p,q,rp,q,r such that whenever a1,a2,a3,⋯ ,an a_1,a_2,a_3,\cdots,a_n are n n distinct positive integers with the property that at least one of p,q,r p,q,r divides aj−ak ∀1≤j≤k≤n a_j - a_k \ \forall 1\le j\le k\le n, one of p,q,r p,q,r divides all of these differences.
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