Number Theory
# Modular Arithmetic Operations

Which of the following is correct?

**A.** $\ 2^{-1} \equiv 3 \pmod{7}$

**B.** $\ 3^{-1} \equiv 4 \pmod{7}$

**C.** $\ 5^{-1} \equiv 2 \pmod{7}$

**D.** $\ 6^{-1} \equiv 6 \pmod{7}$

What is $5 ^ {-1} \pmod{17} ?$

**Hint:** Remember that inverses multiply to 1.

What is

$\large 14^{-1} \pmod{17} ?$

What is $\large 10! \pmod{11}?$

What is $2 ^ {-1} \pmod{39} ?$

**Note:** $2^{-1} \pmod{39}$ is the integer $k$ such that $2 \times k \equiv 1 \pmod{39}.$