if ((2^n) -1 ) is prime, prove n is prime ?! >.<
Ok heres the question! :
if (2^n) -1 ) is prime, prove n is prime
i have attempted this question. However, i do not knw if i have started it off right, below is what i have done so far:
Suppose n is COMPOSITE, and let n = rs, where r, s >1
hence, ((2^n) -1 ) becomes if ((2^rs) -1 )
((2^rs) -1 )=((2^s) -1 ) (1 + (2^s) +(2^2s)+(2^3s)+...+(2^s(r-1)) )
so ((2^s) - 1) | ((2^n) -1 )
since ((2^n) -1 ) is prime .....
then after this i dont know what to do, if possible could someone please tell me how to continue please or a hint or something.
thankyou very much in advance, CoCo_RoAcH ^^