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 \(2 \times k \equiv 1 \pmod{39}.\)

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