MathDB

For positive integers

n

and

k \geq 2

, define

E_k(n)

as the greatest exponent

r

such that

k^r

divides

n!

. Prove that there are infinitely many

n

such that

E_{10}(n) > E_9(n)

and infinitely many

m

such that

E_{10}(m) < E_9(m)

N3