Mod problem

[buckaroobill]

i'm not sure how to do the problem below because my book doesn't explain how to do this type of problem well so if anyone could show me, i'd appreciate it.

for modulo 17, find x so that [5] * [x] = [13]

 

[pka]

We want \(\displaystyle 5x - 13\) to be divisible by 17.
Now if \(\displaystyle x = 6\) we have one solution.
Also if \(\displaystyle x = {23}\) we have another solution.
Moreover, if \(\displaystyle x = - {11}\) we also have a solution.

\(\displaystyle \left[ 6 \right] = \left\{ {n:n = 6 + 17k\quad k \in Z} \right\}.\)

 

[buckaroobill]

thanks! but how did you arrive at those solutions?

 

[pka]

how did you arrive at those solutions?

Do you understand the modulo relation?

 

[buckaroobill]

OHHH! I get it now! Sorry. It took me a few minutes to see what was happening, but now I do. Thanks so much for all your help!