(2^x)/(a*2^y)

[Flofloflo]

Hello,
Searching for divisors I figured divisors of 2^x can only be divided by other numbers that can be written as 2^y, 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...

[simplethinker]

Think of it this way: Any integer can be written as N=p₁^a₁p₂^a₂...p_r^a_r, where all the p_r'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=2^b₁3^b₂5^b₃ where 0≤b₁≤3, 0≤b₂≤2 and 0≤b₃≤1

[Flofloflo]

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