XleonardXcobetX@gmail.com wrote: > I cannot seem to find a power of 2 divisible by 3. I did all of the > powers up to 4096 in my head. Then I wrote a simple computer program > to try to find a power of 2 divisible by 3, but it couldn't find any. > So the number must be above 2^32. But what is the smallest power of 2 > divisible by 3? Does a number x such that log2(x) is an integer and > x/3 is an integer even exist? Is there a way I might go about proving > or disproving the existence of such a number?
As mentioned by others, there is no such number.
However, powers of 2 alternate between being congruent to 1 (mod 3) and 2 (mod 3) depending on whether the power is even or odd.
So what you can say is:
If n is even, all 2**n - 1 are divisible by 3. If n is odd, all 2**n + 1 are divisible by 3.