Quote:
Originally Posted by MatWurS530113
Many thanks for your reply. But 2 things I don't understand:
1) if why does this imply that for some k? (Probably I miss an easy thought... )

Because
means that m divides a power of 2, namely,
. Therefore,
for some k.
Quote:
Originally Posted by MatWurS530113
2) if n is even I still don't see why n must have the form , if is divisible by (not only by ).

If
then
, and I showed that the latter congruence implies n=2^(k+1)+2 for some k.