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Topic: Power of 2 divisible by 3
Replies: 19   Last Post: Feb 1, 2006 10:37 PM

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AntiGag@gmail.com

Posts: 2
Registered: 1/30/06
Re: Power of 2 divisible by 3
Posted: Jan 31, 2006 1:51 AM
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Correct. First 2 ^ 0 = 1, 1 - 1 = 0 and 2 ^ 1 = 2, 2 + 1 = 3. Second
for any x = 3 * k + 1, 2 * x = 3 * ( 2 * k) + 2 and for any x = 3 * k +
2, 2 * x = 3 * ( 2 * k + 1) + 1, which means for any x = 1( mod 3), 2 *
x = 2( mod 3) and for any x = 2( mod 3), 2 * x = 1( mod 3). Here we
come to the conclusion "If n is even, all 2**n - 1 are divisible by 3.
If n is odd, all 2**n + 1 are divisible by 3."




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