I sada zabava već prilazi kraju, no vrijeme je za grandiozno finale predstave!.
Fibonacci je za kraj odlučio iznenaditi sve gledatelje odabirom zadatka koje je pripremio njegov dragi prijatelj
Diofant. Zadatak dostojan velikog finala i uzbudljive završnice za naše mlade matematičare. A taj zadatak je:
Neka su 
i 
prirodni brojevi manji od 
koji zadovoljavaju jednadžbu 
Odredite najveću moguću vrijednost izraza 
The party is now nearing its end. So it is the time for the final task of the show!
Fibonacci decided for the grand finale to suprise the audience with a task that his good friend
Diofant had crafted. This task is worthy of the grand finale spot and it is a perfect ending of the party for young and enthusiastic mathematicians. The task iiiissss:
Let and be natural numbers smaller than which are solutions to the equation Find the largest possible value of
[lang=hr]
I sada zabava već prilazi kraju, no vrijeme je za grandiozno finale predstave!. \emph{Fibonacci} je za kraj odlučio iznenaditi sve gledatelje odabirom zadatka koje je pripremio njegov dragi prijatelj \emph{Diofant}. Zadatak dostojan velikog finala i uzbudljive završnice za naše mlade matematičare. A taj zadatak je:
Neka su $a$ i $b$ prirodni brojevi manji od $2025$ koji zadovoljavaju jednadžbu $$(a^2-ab-b^2)^2=1$$
Odredite najveću moguću vrijednost izraza $ab$
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[lang=en]
The party is now nearing its end. So it is the time for the final task of the show! \emph{Fibonacci} decided for the grand finale to suprise the audience with a task that his good friend \emph{Diofant} had crafted. This task is worthy of the grand finale spot and it is a perfect ending of the party for young and enthusiastic mathematicians. The task iiiissss:
Let $a$ and $b$ be natural numbers smaller than $2025$ which are solutions to the equation $$(a^2-ab-b^2)^2=1$$
Find the largest possible value of $ab$
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