Each question of this quiz consists of a mathematical expression. Answer by entering the value of the expression, which in each case must be a non-negative integer that is less than the modulus. Enter nothing else, as this is being graded by a computer. (A few of these might not make sense until Tuesday's lecture.)

a) 12 mod 5

b) 5 mod 12

c) (7 + 8) mod 11

d) (7 - 8) mod 11

e) (7 8) mod 11

f) 4³ mod 7

g) gcd(72, 30)

h) 4-1 (mod 9)

Note: This is asking for the modular multiplicative inverse of 4, when working mod 9. The answer is NOT 1/4. To obtain the answer, solve for x in this equation: 4x = 1 (mod 9)

i) 11-1 (mod 65)

Note: This is asking for the modular multiplicative inverse of 11, when working mod 65. The answer is NOT 1/11. To obtain the answer, solve for x in this equation: 11x = 1 (mod 65)

j) 135^{3487384738473873} (mod 136)