8

Part of 2019 Bangladesh Mathematical Olympiad

Problems(1)

BdMO National Higher Secondary 2019/8

Source: BdMO National Higher Secondary 2019/8

The set of natural numbers

\mathbb{N}

are partitioned into a finite number of subsets.Prove that there exists a subset of

S

so that for any natural numbers

n

,there are infinitely many multiples of

n

S

pigeonhole principlecombinatorics