MathDB
China 2010 quiz3 problem 3

Source:

September 11, 2010
pigeonhole principleceiling functionnumber theory unsolvednumber theory

Problem Statement

Let k>1k>1 be an integer, set n=2k+1n=2^{k+1}. Prove that for any positive integers a1<a2<⋯<ana_1<a_2<\cdots<a_n, the number ∏1≤i<j≤n(ai+aj)\prod_{1\leq i<j\leq n}(a_i+a_j) has at least k+1k+1 different prime divisors.
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