# Find all solutions of x2 + x +1 ≡ 0 (mod 11) etc..

Number Theory - Polynomial Congruences

Find all solutions of each of the following congruences .

(a) x2 + x +1 ≡ 0 (mod 11)

(b) x3 + x + 1 ≡ 0 (mod 13)

(c) x4 + x3 + 2 ≡ 0 (mod 7)

See attached file for full problem description.

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#### Solution Summary

This solution is comprised of a detailed explanation for solving the problems on polynomial congruences.

It contains step-by-step explanation for finding all solutions of each of the following congruences:

(a) x2 + x +1 ≡ 0 (mod 11)

(b) x3 + x + 1 ≡ 0 (mod 13)

(c) x4 + x3 + 2 ≡ 0 (mod 7)

Solution contains detailed step-by-step explanation.