Marinada '22

[lang=hr] Definiramo $\emph{umor}$ uređene trojke prirodnih brojeva $(a,b,c)$ kao zbroj $a+b+c$. Uređena trojka prirodnih brojeva $(c,i,f)$ zove se $\emph{nenaspavana}$ ako zadovoljava jednadžbu $$ c^3 - 7^i3^f= 8 $$ Odredi umnožak umora svih nenaspavanih trojki :) \\ Npr. ako su tražene trojke $(1,2,3)$ i $(4,5,6)$, rješenje je $(1+2+3)\cdot(4+5+6)=90$. [/lang] [lang=en] Define $\emph{tiredness}$ of an ordered triple of positive integers $(a,b,c)$ as sum $a+b+c$. Ordered triple of positive integers $(c,i,f)$ is said to be $\emph{sleepless}$ if it satisfies the equation $$ c^3 - 7^i3^f= 8 $$ Determine the product of tiredness' of all sleepless triples :) \\E.g. if triples $(1,2,3)$ and $(4,5,6)$ satisfy given condition, the solution is $(1+2+3)\cdot(4+5+6)=90$. [/lang]