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Does n² has all the factors n has? How can I be sure?by MonkeyKid
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#1
Mar2214, 12:29 PM

P: 25

First of all, pardon me for my poor English, which is even worse for mathematics.
As an answer to my question, I think it does have all the factors n has. But I can't write mathematical proof of it, and so I can't make that statement. It's probably easy. I can write that in the opposite direction though: let a, b, c, ..., z be the factors of N: (a * b * c * ... * z) = N then (a * b * c * ... * z)² = N² (pretty simple thinking) but I can't write that in the other direction... I mean, begining with N² and it's factors, conclude that it has at least all the factors N has. 


#2
Mar2214, 12:34 PM

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P: 3,211

Well, let's write ##N = a_1 a_2 \ldots a_n## and choose any factor, say ##a_1##. Then ##N^2 = (a_1 a_2 \ldots a_n)(a_1 a_2 \ldots a_n) = a_1*X## where ##X = (a_2 a_3 \ldots a_n)*N##. Therefore ##a_1## is a factor of ##N^2##.
[edited] to use better notation 


#3
Mar2214, 01:19 PM

P: 25




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