We will solve the following problem (It is problem 3 from NMO 2026, proposed for grade 7 page 5):
Determine the pairs $(a,b)$ of nonzero natural numbers for which the
numbers $\frac{a^2+b}{a+b-1}$ and $\frac{b^2+a}{a+b}$ are natural.
{author} Lucian DRAGOMIR, Oțelu Roșu
Vocabulary : NMO = National Mathematics Olympiad
(in construction)
