It seems like an interesting function. Solutions are \(\displaystyle z \in \mathbb{z} \implies x = \frac{97645643}{6\cdot z+1}\)

Let \(\displaystyle f(x) = 97645643 â€“ 6x \cdot \lfloor \frac{97645643 }{ 6x} \rfloor =x\) and let lpf(n) be the smallest primefactor of a positive integer.

So lpf(4) = 2.

For composite numbers c not or the form \(\displaystyle 2^m \cdot 3^n\), it seems that f(97645643/c) = 97645643/(c/lpf(c)). One might find this helpful to find primefactors. Interesting function you gave.