# Thread: solve polynomial mod p

1. ## solve polynomial mod p

How would I go about solving x^6-9x^4+11x^2+21 = 0 mod 1499 . ? I cant seem to get the right answer by factoring the polynomial.

- Kate

2. The polynomial factorises over the integers as $(x^2-3)(x^2-7)(x^2+1)$. To see whether any of the quadratic factors can be further factorised mod 1499, you need to test whether the numbers 3, 7 and –1 are quadratic residues mod 1499.