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

Imcool Jan 6, 2023

#2**0 **

13(3x - 2) =26 (mod 8)..............(1)

Divide both sides by 13

(3x - 2) =2 (mod 8)

3x =4 (mod 8) - this is the same as (1) above

x =8m + 4, where m=0, 1, 2, 3........etc. [This is the full solution]

So, when m=0, x =4

And when m=1, x =(8*1 + 4) =12

Guest Jan 6, 2023