Nastavljajući svoj put Petar otkriva novi satelitEgzotični izgled ovog satelita privlači ga da ga istraži
Pritajen od ostalih svemirskih objekata
Tajni satelit zapravo je prekriven očaravajućom prirodom
U ovom satelitu mogu se naći tulipani, ruže, orhideje,...
No, ovdje se nalazi i sljedeći Petrov zadatak
Nađi sve nenegativne cjelobrojne parove 
tako da su oba sljedeća izraza cijeli brojevi 
Kao rješenje nađi zbroj svih vrijednosti 
koje dobiješ(ako se neka vrijednost ponavlja u više različitih parova, onda se toliko puta zbraja) i dodaj tome 
da dobiješ rješenje
New adventures on a different satellite now await Peter Egzotic beauty draws him to explore
Pretty sights he would never expect to find here
This secret satellite is covered by breathtaking nature
Under the huge trees one finds so many rare plants
Numerous kinds of beautiful flowers like roses and tulips
Even though it is so pretty here, Peter wants to solve this next task and continue
Find all non-negative pairs so that both of the following expressions are integers For the solution of this problem find the sum of all the values for that you find(if a certain value appears in multiple pairs, you add it that value for each its occurence) and then add to it to get the solution.
[lang=hr]
\emph{Nastavljajući svoj put Petar otkriva novi satelit}
\emph{Egzotični izgled ovog satelita privlači ga da ga istraži}
\emph{Pritajen od ostalih svemirskih objekata}
\emph{Tajni satelit zapravo je prekriven očaravajućom prirodom}
\emph{U ovom satelitu mogu se naći tulipani, ruže, orhideje,... }
\emph{No, ovdje se nalazi i sljedeći Petrov zadatak}
Nađi sve nenegativne cjelobrojne parove $(a,b)$ tako da su oba sljedeća izraza cijeli brojevi $$\frac{a^2+b}{b^2-a} \quad \text{i} \quad \frac{b^2+a}{a^2-b}$$ Kao rješenje nađi zbroj svih vrijednosti $a$ koje dobiješ(ako se neka vrijednost ponavlja u više različitih parova, onda se toliko puta zbraja) i dodaj tome $2$ da dobiješ rješenje
[/lang]
[lang=en]
\emph{New adventures on a different satellite now await Peter }
\emph{Egzotic beauty draws him to explore}
\emph{Pretty sights he would never expect to find here}
\emph{This secret satellite is covered by breathtaking nature}
\emph{Under the huge trees one finds so many rare plants }
\emph{Numerous kinds of beautiful flowers like roses and tulips}
\emph{Even though it is so pretty here, Peter wants to solve this next task and continue}
Find all non-negative pairs $(a,b)$ so that both of the following expressions are integers $$\frac{a^2+b}{b^2-a} \quad \text{i} \quad \frac{b^2+a}{a^2-b}$$ For the solution of this problem find the sum of all the values for $a$ that you find(if a certain value appears in multiple pairs, you add it that value for each its occurence) and then add $2$ to it to get the solution.
[/lang]
