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)

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.

chinese remainder theorem

Find all solutions of the problem of Sun-Tsu. Find all integers x such that the remainder after division by 3 is equal to 2, the remainder after division by 5 is equal to 3, the remainder after division by 7 is equal to 2

chinese remainder theorem and proofs

question is attached as a microsoft word document

Congruences

In Z135, the element [4] is a unit. Why? Find the multiplicative inverse [4]^-1 (Please see attachment for proper format)

Proof of sum convergence for relative primes

See attached file