
Re: Power of 2 divisible by 3
Posted:
Jan 31, 2006 1:51 AM


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."

