If a ^ n - 1 is a prime, prove that a = 2 and N is a prime | Math enthusiast | Mathematical art

If a ^ n - 1 is a prime, prove that a = 2 and N is a prime

Let me have a try. Maybe it's not the simplest proof method for reference. This proof has two conclusions. We need to prove them separately. Here I use the counter proof method. First, suppose that a is not equal to 2, then a = 1 or a > 2. When a = 1, a ^ n-1 = 0 is not a prime. Obviously, it's wrong. When a > 2, a ^ n-1 = (A-1) (a ^ (n-1) + A ^ (n-2) +... + 1)

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