4

Part of 2007 Danube Mathematical Competition

Problems(1)

Danube Mathematical Competition 2007 Problem 4

Source: Beautiful problem with beautiful combinatorial solution

a,n

be positive integers such that a\ge(n\minus{}1)!. Prove that there exist

n

distinct prime numbers

p_1,\ldots,p_n

so that p_i|a\plus{}i, for all i\equal{}\overline{1,\ldots,n}.

number theoryprime numbersnumber theory proposed