MathDB
Danube Mathematical Competition 2007 Problem 4

Source: Beautiful problem with beautiful combinatorial solution

December 8, 2007
number theoryprime numbersnumber theory proposed

Problem Statement

Let a,n a,n be positive integers such that a\ge(n\minus{}1)!. Prove that there exist n n distinct prime numbers p1,…,pn p_1,\ldots,p_n so that p_i|a\plus{}i, for all i\equal{}\overline{1,\ldots,n}.
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