1. Find all solutions (a) 2x + 3 = 7 (b) 2x + 3 = 7 to the following congruences.. (mod 9) (mod 20)

1. For each solution. JX² = -1 (mod 397) (397 is prime) CO congruence determine whether there is a x² +8x + 14 = 0 (mod 37) ししし iii) x² = 785 (mod 787) (787 is prime)

2. Solve the simultaneous congruences x = 4 (mod 5) and 2x = 3 (mod 7)

True or false: If a and b are integers satisfying 4a congruent 4b(mod 20), then a congruent b (mod 5). Justify your answer