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