These are the number theory questions.

I have no clue how to do these.

Please explain to me step by step.

Thank you

2. Suppose (1,5, and c are integers. Prove that ifa | b and a. | c then a. | b + c and a. | b c. 4. What is the largest in. such that 16 and 25 are in the same remainder class modulo R? Write out the remainder class they both belong to and give an example of a number more than 100 in that class. 8. Determine which of the following congruences have solutions, and find any solutions (between 0 and the modulus) by trial and error. a. 4:1: E 5 (mod 6). b. 632 E 3 (mod 9). C. m2 E 2 (mod 4)