Marinada '24

[lang=hr] Nakon neuspjeha na prošlom zadatku, odlučio je više se potruditi na idućem zadatku:\\ Find all integer triples $(a,b,c)$ with $a>0>b>c$ whose sum equal $0$ such that the number $$N=2017-a^3b-b^3c-c^3a$$is a perfect square of an integer.\\ Zadatak nije lagan pa je na njega potrošio cijeli put kroz Bestovje. Okušajte se i vi! (rješenje napišite u obliku "(suma svih mogućih $a$, suma svih mogućih $b$, suma svih mogućih $c$)") [/lang] [lang=en] After the failure with the previous problem, Fran decided to put in more effort on the next one: Find all integer triples \((a, b, c)\) with \(a > 0 > b > c\) whose sum equals 0, such that the number \[ N = 2017 - a^3b - b^3c - c^3a \] is a perfect square of an integer. The problem wasn't easy, and Fran spent the entire journey through Bestovje working on it. Now, it's your turn to give it a try! (Write the solution in the form "(sum of all possible \(a\), sum of all possible \(b\), sum of all possible \(c\))"). [/lang]