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even divisors of 2048 #89855
09/14/06 09:19
09/14/06 09:19
Joined: Oct 2003
Posts: 4,131
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Matt_Aufderheide Offline OP
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Matt_Aufderheide  Offline OP
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Are there any even divisors of 2048 between 64 and 128? Is there a method to determine this?


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Re: even divisors of 2048 [Re: Matt_Aufderheide] #89856
09/14/06 11:04
09/14/06 11:04
Joined: Jul 2000
Posts: 27,935
Frankfurt
jcl Offline

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jcl  Offline

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Posts: 27,935
Frankfurt
I think you can prove that 2048 can not have an even divisor between 64 and 128:

2048 is 2*2*2...*2. Suppose it had an even divisor u that is not a power of 2, then 2048 = u*v = (2*2*2..*n)*(2*2*2..*m) = (2*2*2..)*(m*n), while n and m both are >1 and odd. This however is not possible because (m*n) then is also odd and can't result in 2048 when multiplied with a power of 2.

Re: even divisors of 2048 [Re: jcl] #89857
09/15/06 05:27
09/15/06 05:27
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Matt_Aufderheide Offline OP
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While of course I dont undrstand your proof, you are right ..


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Re: even divisors of 2048 [Re: Matt_Aufderheide] #89858
09/15/06 23:27
09/15/06 23:27
Joined: Oct 2005
Posts: 4,771
Bay City, MI
lostclimate Offline
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lostclimate  Offline
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i now have a headache because i read this goood job, i blame you doug... im gonna go get some coffee now.

Re: even divisors of 2048 [Re: jcl] #89859
09/17/06 03:26
09/17/06 03:26
Joined: Mar 2001
Posts: 3,298
Beverly, Massachusetts
Rhuarc Offline
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Quote:

I think you can prove that 2048 can not have an even divisor between 64 and 128:

2048 is 2*2*2...*2. Suppose it had an even divisor u that is not a power of 2, then 2048 = u*v = (2*2*2..*n)*(2*2*2..*m) = (2*2*2..)*(m*n), while n and m both are >1 and odd. This however is not possible because (m*n) then is also odd and can't result in 2048 when multiplied with a power of 2.




Get off your mathematician ass and go rollerblading... you make our heads hurt

Nice one, Doug. Gotta admit though, I recognize what you're doing, but don't have the slightest idea how it's actually figured mathematically anymore.

-Rhuarc


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Re: even divisors of 2048 [Re: Rhuarc] #89860
09/17/06 09:32
09/17/06 09:32
Joined: Jan 2004
Posts: 2,013
The Netherlands
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Excessus Offline
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The Netherlands
Code:

IsEvenDivisor(Divisor, Value)
{
return Value / Divisor == int(Value / Divisor)
}

..
i = 65;
while(i < 128)
{
if(IsEvenDivisor(i, 2048))
{
EvenDivisors += 1;
}
i += 1;
}



KISS. Keep it simple, stupid


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