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Let n be the integer such that \( 0 \le n < 31\) and \(3n \equiv 1 \pmod{31}\). What is \(\left(2^n\right)^3 - 2 \pmod{31}\)?

Express your answer as an integer from 0 to 30, inclusive.

 Dec 14, 2020
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3n mod 31 = 1, solve for n

 

n = 31m  +  21, where m =0, 1, 2, 3........etc.

 

The smallest n = 21

 

[(2^21)^3  -  2] mod 31 == 6

 Dec 14, 2020

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