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# Inverse

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Find the modular inverse of 27, modulo 29. Express your answer as an integer from 0 to 28, inclusive.

Oct 14, 2022

#1
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modular inverse of 27 modulo 29 = 14

27 mod 29 = 27

[14 * 27] mod 29 = 1

Oct 14, 2022
#2
+118132
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Thanks guest.

14 is correct.  I think guest did it with a calculator.

This is fine but I will give a non-calculator answer

Find N such that  27*N (mod29) = 1

$$27\equiv-2 \mod 29\\ 30\equiv 1 \mod 29\\ -2*-15 = 30 \equiv 1 \mod29\\ -15\equiv 29-15 \mod29 \equiv 14 \mod29\\ so\\ 27*14=1 \mod29\\ \text{So 14 is the modular inverse of 27 (mod 29)}$$

Oct 15, 2022