Answer
a) 10
b) 5
c) 8
d) 10
e) 5
f) 3
Work Step by Step
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
