Let be two natural numbers. When we divide by , we the the remainder and the quotient Determine all pairs for which
%V0
Let $a,b$ be two natural numbers. When we divide $a^2+b^2$ by $a+b$, we the the remainder $r$ and the quotient $q.$ Determine all pairs $(a, b)$ for which $q^2 + r = 1977.$
Source: Međunarodna matematička olimpijada, shortlist 1977
Školjka 
be two natural numbers. When we divide 
by 
, we the the remainder 
and the quotient 
Determine all pairs 
for which 