Marinada '22

[lang=hr] Vraćamo se na trojke prirodnih brojeva, gdje je $f$ prost te vraćamo i početnu definiciju umora $c+i+f$. Trojka je nenaspavana ako su istovremeno zadovoljene sljedeće dvije jednadžbe: $$f+1=2c^2$$ $$f^2+1=2i^2$$ Odredite umnožak umora svih nenaspavanih trojki. [/lang] [lang=en] Looking back at triples of only positive integers where $f$ is prime and our first definition of tiredness $c+i+f$. Triple is said to be sleepless if it satisfies both of the following equations: $$f+1=2c^2$$ $$f^2+1=2i^2$$ Determine the product of tiredness' of all sleepless triples. [/lang]