Marinada '22

[lang=hr] Dan je prost broj $p$. Neka je $f(p)$ broj uređenih četvorki $(a, b, c, d)$ prirodnih brojeva koji nisu djeljivi s $p$ koje zadovoljavaju jednadžbe $ac + bd = p(a + c)$ i $bc - ad = p(b - d)$. Odredi zbroj $f(p)$ za sve proste $p<10^7$, tj. $\sum_{p\text{ prost}}^{p < 10^7} f(p)$ . [/lang] [lang=en] There is a prime number $p$. Let $f(p)$ be the number of ordered fours $(a, b, c, d)$ of natural numbers that are not divisible by $p$ that satisfy the equations $ac + bd = p(a + c)$ and $bc - ad = p(b - d)$. Find the sum of $f(p)$ for all prime $p<10^7$, that is $\sum_{p\text{ prost}}^{p < 10^7} f(p)$. [/lang]