## Discrete Mathematics and Its Applications, Seventh Edition

Suppose that $a$ and $b$ are integers, $a$≡11 mod 19 and $b$≡3 mod 19. Find the integer $c$ with 0≤$c$≤18 s.t. a) $c≡13a$ mod 19 $c≡143$ mod 19≡19(7)+10 mod 19 b) $c≡8b$ mod 19 $c≡24$ mod 19≡19(1)+5 mod 19 c) $c≡a−b$ mod 19 $c≡8$ mod 19 d) $c≡7a+3b$ mod 19 $c≡86$ mod $19≡19(4)+10$ mod 19 e) $c≡2a^2+3b^2$ mod 19 $c≡269$ mod $19≡14(19)+5$ mod 19 f) $c≡a^3+4b^3$ mod 19 $c≡12429$ mod $19≡654(19)+3$ mod 19