Thread: Proof... please help.

If pq|(n^2) proof that pq|n...
p is prime and q is prime and pis not equal to q.

My proof I used the contrapositive to proof it..
if pq not divisble by n then pq is not divisible by n squared
*!= is not equal to..
Short version of proof
n!=pqk where k is element of Z
(n)^2 !=pqc where c=kpq is element of Z

please check if this is right...
How will you prove this directly?

Originally Posted by Dreamer78692

If pq|(n^2) proof that pq|n...
p is prime and q is prime and pis not equal to q.

My proof I used the contrapositive to proof it..
if pq not divisble by n then pq is not divisible by n squared
*!= is not equal to..
Short version of proof
n!=pqk where k is element of Z
(n)^2 !=pqc where c=kpq is element of Z

please check if this is right...
How will you prove this directly?

Please note that means " or , and not the other way around.

Now, you only wrote the contrapositive of your problem, but you didn't provide any proof...

I'd go like this: write n as a producto of powers of primes: ,so:

, and from the uniqueness (up to order) of

the representation as a product of primes, it must be that , for some indexes . Take it from here.

Tonio

I cant believe I never think of that thanks man....