Let be a number that is not a prime. Show that there is a divisor of , with , so that On my paper, I've written down n=rs where n and s are any natural numbers >1. Not sure if that's needed, though.
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Originally Posted by Joel24 Let be a number that is not a prime. Show that there is a divisor of , with , so that On my paper, I've written down n=rs where n and s are any natural numbers >1. Not sure if that's needed, though. If n>2 is not prime, then it has a factor p>=2, so there also exists a q>=2 such that pq=n. Now if both n<p^2 and n<q^2, then pq<n a contradiction. Hence every composite number >2 has a factor whose square is less than or equal to the number. RonL
Ah, a proof (or sorts) by contradiction. I would've never have thought of that. Excellent. Thank you so much!
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