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What is the sum of all positive integer solutions less than or equal to 20 to the congruence 13(3x-2) == 26 - x (mod 8)?

 May 30, 2022
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What is the sum of all positive integer solutions less than or equal to 20 to the congruence 13(3x-2) == 26 - x (mod 8)?

 

13(3x-2) == 26 - x (mod 8)?

 

26-x (mod8) == 2-x (mod8)

 

13(3x-2) mod8 == 5(3x-2) (mod8) == 15x-10 (mod8) == -x-2 (mod8) == -2-x (mod 8)

 

So it doesn't like like there are any values of x.

 

I designed a little excel table to check

 

 May 30, 2022

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