Could you please help me with this question and explain it?

2. In this question, you may use the fact that 541 | 2032 - 93. (a) Let x E Z. Using the fact that 541 is prime, show that x2 = 93 mod 541 x = 203 mod 541 or *= -203 mod 541 That is, show that x satisfies the first congruence if and only if it satisfies the second or the third. You should make it clear how you use the primality of 541. Hint: Take the 93 over to the other side of the congruence. (b) Find the first four positive integers x satisfying the simultaneous con- gruences x =93 mod 541 x = 3 mod 200 Show your working. A brute-force search will not count