) Use the Chinese Remainder Theorem to find all solutions be- tween 0 and 1000 satisfying the following system of linear con- gruences: x = 1 x = 2 x = 3 x = 4 (mod 2) (mod 3) (mod 5) (mod 7).

Find the solutions of x and y to the following pair of linear equations: 7× + 3y = 5 (mod 11) 4x +2y = 3 (mod 11) Show important intermediate steps.

Use the Chinese remainder theorem to solve the system x = 3 mod 5 x = 5 mod 11