IMO 2023 Shortlist N3
For positive integers n and k ě 2 define Ekpnq as the greatest exponent r such that kr divides n!. Prove that there are ...
Category: Number Theory
Problem
For positive integers n and k ě 2 define Ekpnq as the greatest exponent r such that kr divides n!. Prove that there are infinitely many n such that E10pnq ą E9pnq and infinitely many m such that E10pmq ă E9pmq. (Brazil)