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Flofloflo


Member


Joined: 07 Nov 2007
Posts: 120

Posted: 26 Feb 2009 06:59:26 am    Post subject:

Hello,
Searching for divisors I figured divisors of 2x can only be divided by other numbers that can be written as 2y, and I think that goes for other powers and stuff too, but it seems impossible to prove...

Does anybody have a clue how to prove it?? I tried writing things as logaritms and all, but I suppose the only way to prove it is to use similar methods like proving sqrt(2) doesn't have divisors but we barely do that yet at school, so I have absolutely no idea how to start on this...
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simplethinker
snjwffl


Active Member


Joined: 25 Jul 2006
Posts: 700

Posted: 26 Feb 2009 11:01:47 am    Post subject:

Think of it this way: Any integer can be written as N=p1a1p2a2...prar, where all the pr's are primes. A number M can only be a divisor of N if and only if its set prime factors is a subset of Ns prime factors and the exponents are less than or equal to the powers in N. For example, 360=233251. Any divisor D of 360 must then be of the form D=2b13b25b3 where 0≤b1≤3, 0≤b2≤2 and 0≤b3≤1

Quote:
but I suppose the only way to prove it is to use similar methods like proving sqrt(2) doesn't have divisors but we barely do that yet at school, so I have absolutely no idea how to start on this...

It's actually a different approach. With sqrt(2), you're dealing with the existence of factors, but with this you're dealing with the form of the factors.
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Flofloflo


Member


Joined: 07 Nov 2007
Posts: 120

Posted: 26 Feb 2009 02:37:13 pm    Post subject:

Okay, thanks!
It keeps amazing me how much stuff you can do with primes:P
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