IMO Shortlist 2007 problem N7


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 9,0
Dodao/la: arhiva
2. travnja 2012.
LaTeX PDF
For a prime p and a given integer n let \nu_p(n) denote the exponent of p in the prime factorisation of n!. Given d \in \mathbb{N} and \{p_1,p_2,\ldots,p_k\} a set of k primes, show that there are infinitely many positive integers n such that d|\nu_{p_i}(n) for all 1 \leq i \leq k.

Author: Tejaswi Navilarekkallu, India
Izvor: Međunarodna matematička olimpijada, shortlist 2007