Re: [PrimeNumbers] obvious???
- On 1/16/07, leavemsg1 <leavemsg1@...> wrote:
> Is it entirely obvious that 2^(p-1)+3^(p-2) -1 is always divisible by 2Yes.
> and 3 where p is prime???
2^whatever is even, 3^whatever is odd, so 2^x + 3^y - 1 is even.
2^even = 1 (mod 3), 3^whatever = 0 (mod 3), so
2^even + 3^whatever - 1 is divisible by 3.
So if p is odd (not necessarily prime, and not 2), then the
divisibility will happen as you have said.