Suppose a and b are integers, a ≡ 11 (mod 19) and b ≡ 3 (mod 19). Find an integer c with 0≤c≤18 such that (a)c≡13a(mod 19). (b)c≡8b(mod 19). (c)c≡a-b(mod 19). (d)c≡7a+ 3b(mod 19). (e)c≡2a^2+ 3b^2(mod 19). (f)c≡a^3+ 4b^3(mod 19).

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a.) $13*11=143$

$143=10(mod 19)$

b.) $8*3=24$

$24=5(mod 19)$

c.) $a-b=11-3=8(mod19)$

d.) $77+9=1+9=10(mod19)$

e.) $2*11^2+3*3^2= 2*7+3*9=14+27=41=3(mod 19)$

f.) $11^3+4*3^3=7*11+3*3*9=1+5=6(mod19)$