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Which of the following is correct?
A. 2 − 1 ≡ 3 ( m o d 7 ) \ 2^{-1} \equiv 3 \pmod{7} 2−1≡3(mod7)B. 3 − 1 ≡ 4 ( m o d 7 ) \ 3^{-1} \equiv 4 \pmod{7} 3−1≡4(mod7)C. 5 − 1 ≡ 2 ( m o d 7 ) \ 5^{-1} \equiv 2 \pmod{7} 5−1≡2(mod7)D. 6 − 1 ≡ 6 ( m o d 7 ) \ 6^{-1} \equiv 6 \pmod{7} 6−1≡6(mod7)
What is 5 − 1 ( m o d 17 ) ? 5 ^ {-1} \pmod{17} ? 5−1(mod17)?
Hint:Remember that inverses multiply to 1.
What is
1 4 − 1 ( m o d 17 ) ? \large 14^{-1} \pmod{17} ? 14−1(mod17)?
What is 10 ! ( m o d 11 ) ? \large 10! \pmod{11}? 10!(mod11)?
What is 2 − 1 ( m o d 39 ) ? 2 ^ {-1} \pmod{39} ? 2−1(mod39)?
Note: 2 − 1 ( m o d 39 ) 2^{-1} \pmod{39} 2−1(mod39)is the integer k k ksuch that 2 × k ≡ 1 ( m o d 39 ) . 2 \times k \equiv 1 \pmod{39}. 2×k≡1(mod39).
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