MathDB

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\mid \nu_{p_i}(n)

for all

1 \leq i \leq k

.
Author: Tejaswi Navilarekkallu, India

Problem Statement