How to transform an equation with mod()?

Question

Mathematics

r = x*k % 32;
How to transform this equation to find x?

Answer 1

r = (k * x) % 32
k * x = 32 * i + r, i ∈ ℤ _≥0
x = (32 * i + r) / k, i ∈ ℤ _≥0
for the mod operation with negative numbers.

Answer 2

It will not be possible to transform this equation, because there is no inverse operation for mod, because there will be a set of x values.
You can find them like this:

for (int x, x<1000, x++)
 {
  if r==(x*k)%32 then cout << x << ', ';
 }

Answer 3

No way.