MathDB

2.2

Part of MathLinks Contest 7th

Problems(1)

0722

Source:

4/28/2008
For a prime p p an a positive integer n n, denote by νp(n) \nu_p(n) the exponent of p p in the prime factorization of n! n!. Given a positive integer d d and a finite set {p1,p2,…,pk} \{p_1,p_2,\ldots, p_k\} of primes, show that there are infinitely many positive integers n n such that νpi(n)≡0(modd) \nu_{p_i}(n) \equiv 0 \pmod d, for all 1≤i≤k 1\leq i \leq k.
modular arithmeticvectornumber theoryprime factorization