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Algebraic factors? (Posted on 2021-07-28)

Determine all natural numbers n such that n¹⁰ + n⁵ + 1 is prime.

No Solution Yet Submitted by Danish Ahmed Khan

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solution by factoring

| Comment 2 of 3 |

n^10 + n^5 + 1 = (n^2 + n + 1)(n^8 - n^7 + n^5 - n^4 + n^3 - n + 1)

Conjectured after noting first four cases are divisible by 3,7,13,21 and verified by division.

Posted by xdog on 2021-07-28 15:02:16

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