Quote:
Originally Posted by MatWurS530113
if and only if is divisible by then there is a nonnegative Integer k with

Consider two cases:
1) n is even then
.
We have n=2m+2 and
, implying that
for some k. Therefore, n=2*2^k+2=2^(k+1)+2.
2) n is odd then
.
We have n=2m+1 and
, implying that
and
.