IMO 2007 Shortlist N7
For a prime p and a positive integer n, denote by νp(n) the exponent of p in the prime factorization of n!. Given a posi...
Category: Number Theory
Problem
For a prime p and a positive integer n, denote by νp(n) the exponent of p in the prime factorization of n!. Given a positive integer d and a finite set {p1,...,pk} of primes. Show that there are infinitely many positive integers n such that d νpi (n) for all 1 ≤ i ≤ k. (India)