MathDB

4

Part of 1968 Swedish Mathematical Competition

Problems(1)

f(m-n) , where m, n belong to M cannot exceed n-1.

Source: 1968 Swedish Mathematical Competition p4

3/21/2021
For n≠0n\ne 0, let f(n) be the largest kk such that 3k3^k divides nn. If MM is a set of n>1n > 1 integers, show that the number of possible values for f(m−n)f(m-n), where m,nm, n belong to MM cannot exceed n−1n-1.
number theorydivisible