TITLE: multiply solution of linear congruence equation
QUESTION [0 upvotes]: let us consider the following theorem

i am surprised about this  theorem because if  we take for instance following equation

and if we divide both side by 2, we will get

one solution is 3 and another solution is  7, but there  another solution  11, because  $2*11=22$, $22-6=16$  and  definitely $8$ divides  $16$,  there is another solution  $19=3+16$  because $2*19=38$ $38-6=32$ and again  $32$ can be divided by  $8$,  then why is there exactly $d$ solution?in our case $d=2$

REPLY [1 votes]: The point is that 11=3 mod 8 as $11=8 \cdot 1 + 3$.
In general when you find a solution $x$ in a mod $ n $ you can find infinite solution in the form $ x+tn $ with $ t \in N$
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