Ok, the proof to be done is pretty simple:(adsbygoogle = window.adsbygoogle || []).push({});

Prove that a number is a square only when the number of positive divisors is odd.

I pretty sure I know the answer, I'm just not sure how to go about writing it out...

If c is the number then you can write:

c=ab.

a and b are divisors of c. If a doesn't equal b then you have two different divisors. If a=b, then c=ab can be rewritten as c=a^2, and you only have one divisor. Because of this any number that can be written as a square of another number has an odd number of divisors -- all the pairs of factors that equal the number plus the 1 divisor that is squared to make the number.

I guess I just need to know how to write this out better, and how to make sure I haven't assumed to much as given/proven at the outset.

Thanks,

-GM-

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# Homework Help: Need help with a proof on divisors.

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