Let $ a,n$ be positive integers such that $ a\ge(n-1)!$. Prove that there exist $ n$ distinct prime numbers $ p_1,\ldots,p_n$ so that $ p_i|a+i$, for all $ i=\overline{1,\ldots,n}$.
Problem
Source: Beautiful problem with beautiful combinatorial solution
Tags: number theory, prime numbers, number theory proposed