How many positive integers 'n' are there such that [(2)^n + 1] is divisible by 7 ?

2^n+1=7k, k positiv integer

2^n+1=(2³-1)k
2^n=k2³-(k+1)

in the right member of the equation it should:
for the first: k=even to complete a power of 2
for the second: k=odd cu complete an even number by adding 1.

i.e. k=0
so 2^n=-1 (impossible)

Posted by luminita on 2004-01-08 09:56:07