+0  
 
0
102
4
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What is the residue modulo 13 of the sum of the modulo 13 inverses of the first 12 positive integers?

 Dec 16, 2019
 #1
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+1

Sum of the inverses of the first 12 positive integers:

 

1 + 7 + 9 + 10 + 8 + 11 + 2 + 5 + 3 + 4 + 6 + 12 =78

 

78 mod 13 =0

 Dec 16, 2019
 #2
avatar+108790 
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Could you please explain how you got those numbers?

Melody  Dec 16, 2019
 #3
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I have programmed my computer with "Modular Multiplicative Inverse" algorithm which calculates them automatically. It is very similar to the algorithm used in this online calculator:

https://planetcalc.com/3311/

 Dec 16, 2019
 #4
avatar+108790 
0

ok thanks.

Melody  Dec 16, 2019
edited by Melody  Dec 16, 2019

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