For each of the following congruences, determine all the integer solutions z ∈ {0, . . . , 999}. To so this, you should first put the congruence in the form az = b (mod 1000), as we did in going from (2.2) to (2.3) in Example 2.3. Then follow the steps outlined in §2.2.3. Show all your steps (but you may use a calculator to help with the multiplications). Use the extended Euclidean algorithm to compute modular inverses, where necessary.