Canonical representation?

,.good day everyone,.,need ur help with how to prove this,.

Let n>=2 be an integer with canonical representation n=p₁^{a₁}p₂^{a₂}p₃^{a₃}...p_{k}^{a_{k}}. an integer m>=1 is a positive divisor of n if and only if m=p₁^{b₁}p₂^{b₂}p₃^{b₃}...p_{k}^{b_{k}}, where 0<=b_i<=a_i for all 1<=i<=k.

thnx in advance...

Re: Canonical representation?

If is the set of **all** prime numbers, we can express positive integers as unique products

, ,

where are finitely many non zero integers.

If for all evidently . If there exists positive integer such that that is, . By the unique factorization, , hence for all .