6

Part of 2023 Miklós Schweitzer

Problems(1)

Existence of a number with a fixed number of divisors among 1,2,...,n

Source: Miklos Schweitzer 2023, Problem 6

Prove that for all sufficiently large positive integers

n

and a positive integer

k \leq n

, there exists a positive integer

m

k

divisors in the set

\{1,2, \ldots, n\}