Question

Suppose that a and b are integers, a ≡ 11 (mod 19), and b ≡ 3 (mod 19). find the integer c with 0 ≤ c ≤ 18 such that

Answer 1

A. $c$≡$13 *11[19]=143[19]\equiv 7*19+10[19]\equiv 10[19].$
b. $c\equiv8b[19]=24[19]=19+5[19]\equiv 5[19].$
c. $c\equiv a-b[19]\equiv 8[19].$
d. $c\equiv 7a+3b[19]=86[19]\equiv 10[19].$
e. $c\equiv 2a^2+3b^2[19]=269[19]\equiv 3[19].$
f. $c\equiv a^3+4b^3[19]=1439[19]\equiv 14[19].$