SOLUTION: Find all natural n such that n^2 − 1 is a cube of a prime number.

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Question 1018809: Find all natural n such that n^2 − 1 is a cube of a prime number.
Answer by richard1234(7193) About Me  (Show Source):
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Since n^2 - 1 factors to (n-1)(n+1), which is a cube of a prime number, either n-1 = 1 and n+1 = p^3, or n-1 = p and n+1 = p^2. Checking, we see that the only possible value of n is n = 3 (3^2 - 1 = 2^3).