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)?

Guest May 30, 2022

#1**+1 **

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

Melody May 30, 2022