Marinada '25

[lang=hr] Neka $A = \{ 1,2,3,\dots ,2020\}$. Na koliko različitih načina možemo prikazati $A$ kao uniju dvaju skupova koji nemaju zajedničkih elemenata, pri čemu je zbroj elemenata u svakom skupu neka potencija broja $2$? ($A = B \cup C$ i $A = C \cup B$ se računaju kao isti način). [/lang] [lang=en] Given $A=\{1,2,3,\cdots,2020\}$. In how many different ways can we show $A$ as the union of two sets that share no common elements, and the sum of the elements in each set is some power of $2$. ($A=B \cup C$ and $A=C \cup B$ count as the same). [/lang]