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What is 2^{-1} + 2^{-2} + 2^{-3} + 2^{-4} + 2^{-5} + 2^{-6} mod{13}?

Express your answer as an integer from  0 to 12, inclusive.

 Feb 15, 2023
edited by Guest  Feb 15, 2023
 #1
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As a modular inverse, 2^{-1} = 6.

 

Then 2^{-2} = 6^2 = 10

2^{-3} = 6*10 = 60 = 8

2^{-4} = 6*8 = 48 = 9

2^{-5} = 6*9 = 54 = 2

2^{-6} = 6*2 = 12

 

Adding these up, we get 6 + 10 + 8 + 9 + 2 + 12 = 47 = 8 mod 13.

 

The answer is 8. 

 Feb 15, 2023

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