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 $d=2$
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$