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

 Jan 6, 2023
 #2
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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

 Jan 6, 2023
 #3
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Im confused, which one is correct? i feel like the second one but im not sure...

 Jan 6, 2023
 #4
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Guest, im pretty sure you missed one, which is when m = 2, which would result in 20, and it is valid because the sign is less than or equal to.

 Jan 7, 2023

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