3i think u wont need the proof MI.i dono the elegant proof.
5 Answers
11Contradiction is the best method.
Let n be composite.
So it can be written as n = x.y
2^{n}-1 = 2^{x.y}-1 = (2^{x}-1).(1+2^{x}+2^{2x}+...+2^{(y-1).x})
This makes 2^{n}-1 a composite no. whereas it is PRIME.
Hence, n has to be prime when 2n - 1 is prime (but the converse is not always true).
11Just quoting an well-known result....
If ak-1 is a prime, then a=2, and k is a prime.....