If 2^n + 1 is an odd prime for some integer n, prove that n is a power of 2. (h

Step-by-step explanation:

We will prove by contradiction. Assume that is an odd prime but n is not a power of 2. Then, there exists an odd prime number p such that . Then, for some integer ,

Therefore

Here we will use the formula for the sum of odd powers, which states that, for and an odd positive number ,

Applying this formula in 1) we obtain that

.

Then, as we have that is not a prime number, which is a contradiction.

In conclusion, if is an odd prime, then n must be a power of 2.

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step-by-step explanation:

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