Let p be prime. Using Fermat's little theorem, prove that n: 2ᵖ-² +2 x 5ᵖ-² +10ᵖ-² - 1 is a multiple of p if and only if p ≠

Question

Let p be prime. Using Fermat's little theorem, prove that
n: 2ᵖ-² +2 x 5ᵖ-² +10ᵖ-² - 1 is a multiple of p if and only if p ≠ 2,5. [Hint: for p ≠ 2,5, consider 10n.]

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