Discrete Math - Proof of Uniqueness of Prime Factorization

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  1. William Rose
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Thank you for your video. I have one problem. It assumes the p and q are the same numbers.
What if. 20 = 2 × 5 x 7. Obviously not true
And. 20 = 3 x 11. Could be true for a very large number

ie. the p's and q's are different number

sarahwray
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Nice proof, thanks! Even though an additional explanation of why we must have k=m would have been perfect

phukinho
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Sorry to keep going on
What if for some large numbers, the equivalent of
2 × 11 = 3 × 7. Ie p1 is not one of the qs at all

mhafriendshipcenter
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My previous comment regarded p1 being qj. Thank you for replying, I appreciate your help. 
My failure to understand is when you say that since p1 divides n it must be one of the q's you use qj. What if there is a prime that divides n but is not a p or a q.
I think I am starting to understand when I found Euclids lemma, p l ab then p l a or/and p l b

Thank

mhafriendshipcenter