Number Theory

Modular Arithmetic Operations

Modular Arithmetic - Multiplicative Inverses

         

Which of the following is correct?

A.  213(mod7)\ 2^{-1} \equiv 3 \pmod{7}
B.  314(mod7)\ 3^{-1} \equiv 4 \pmod{7}
C.  512(mod7)\ 5^{-1} \equiv 2 \pmod{7}
D.  616(mod7)\ 6^{-1} \equiv 6 \pmod{7}

What is 51(mod17)? 5 ^ {-1} \pmod{17} ?

Hint: Remember that inverses multiply to 1.

What is

141(mod17)? \large 14^{-1} \pmod{17} ?

What is 10!(mod11)? \large 10! \pmod{11}?

What is 21(mod39)? 2 ^ {-1} \pmod{39} ?


Note: 21(mod39)2^{-1} \pmod{39} is the integer kk such that 2×k1(mod39).2 \times k \equiv 1 \pmod{39}.

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