## BdMO National Higher Secondary 2019/8

samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### 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\$ in \$S\$.

samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### Re: BdMO National Higher Secondary 2019/8

Hint
Short Solution
It can also be proved by contradiction as finite×finite not equals to infinite.

soyeb pervez jim
Posts: 21
Joined: Sat Jan 28, 2017 11:06 pm

### Re: BdMO National Higher Secondary 2019/8

May be this answer is not correct as the question asked to prove that there exists a subset \$S\$ such that in \$S\$ there are infinitely many multiples of any natural number \$n\$.

here you have proven for a natural number \$n\$ there is a subset which have infinite multiple of \$n\$. But you have to prove in subset \$S\$ there are infinity many multiples of any natural number \$n\$