# Answer on Combinatorics | Number Theory Question for Sagar

Question #1238

How can I prove that p=(2^k)-1 is prime if k is odd integer except when k=2?

Expert's answer

If k = 2

p = 2^2 -1 = 3 is prime too.

Maybe you should assume k as prime and use for proving the following equation

(x^k) - 1 = (x - 1)*(x^(k-1) + x^(k-2) + ... + x + 1)

p = 2^2 -1 = 3 is prime too.

Maybe you should assume k as prime and use for proving the following equation

(x^k) - 1 = (x - 1)*(x^(k-1) + x^(k-2) + ... + x + 1)

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