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Challenge 276: Make a Prime?

(i) Given that (x4 + x2 + 1)2 = x8 + x4 + 1 + 2x6 + 2x4 + 2x2, express x8 + x6 + x4 + x2 + 1 algebraically as a difference of two squares.

(ii) Find all the values of x for which x8 + x6 + x4 + x2 + 1 is prime. Explain clearly how you know there are no other suitable values for x.

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