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 )

then

((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 ^^