Marinada '22

[lang=hr] Graf, sastavljen od 2022 vrhova imenovanim brojevima $1,2,3,4,...2022$ je zadan tako da su vrhovi $(x,y)$ povezani ako i samo ako vrijedi $x^yy^x\equiv 2 \mod{5}$. Odredi kromatski broj grafa (Kromatski broj je minimalan broj boja potreban da se vrhovi grafa oboje tako da dva susjedna vrha nisu iste boje). NAPOMENA: nijedan vrh grafa nije povezan sam sa sobom. [/lang] [lang=en] Graph, constructed out of 2022 vertices named by the numbers $1,2,3,4,...2022$ contains an edge $xy$ so that the statement $x^yy^x\equiv 2 \mod{5}$ is true. Determine the chromatic number of the graph (Chromatic number is the minimal number of coulors necessary to paint the vertices of a graph so that two neighbouring vertices are not the same coulor). NOTE: a vertex of the graph is not connected to itself. \\ [/lang]