Marinada '22

[lang=hr] Pronađite sve parove prirodnih brojeva za koje vrijedi $$2m^2+n^2=2mn+3n$$ Kao rješenje upišite sumu zbrojeva kvadrata brojeva u paru po svim rješenjima. Primjer: Ako su rješenja $(0,0)$, $(1,1)$ i $(2,0)$, kao rješenje upišite $0^2+0^2+1^2+1^2+2^2+0^2 = 6$. [/lang] [lang=en] Find all pairs of positive integers for which the following holds true:$$2m^2+n^2=2mn+3n$$ As a solution, enter the sum of sums of squares of numbers in pairs over all solutions. E.g. if pairs (0,0), (1,1) and (2,0) are all solutions to the equation, enter $6$ ($0^2+0^2+1^2+1^2+2^2+0^2 = 6$). [/lang]