1

Part of 2020 Turkey MO (2nd round)

Problems(1)

Divisibility condition on the set 1, 2, ... , n^2

Source: Turkey National Mathematical Olympiad 2020 P1

n > 1

be an integer and

X = \{1, 2, \cdots , n^2 \}

. If there exist

x, y

x^2\mid y

in all subsets of

X

k

elements, find the least possible value of

k

combinatoricsTurkeyDivisibility