Marinada '24

[lang=hr] Nakon svog rizzanja, mewanja i mogganja, Baby Gronku je pokucala porezna na vrata. Oh ne! Traže ga da plati ogroman fanum porez, ali što je najgore, nisu mu rekli koliki je porez, nego su mu dali zagonetku pomoću koje mora otkriti. Dali su mu monički (dakle, vodeći koeficijent mu je jedan) polinom $p$ trećeg stupnja takav da je $$|p(1)|=|p(2)|=|p(3)|=|p(5)|=|p(6)|=|p(7)|$$ i rekli su mu da je fanum porez jednak vrijednosti $|p(0)|.$ Pomozite Baby Gronku otkriti koliki fanum porez mora platiti!!! [/lang] [lang=en] After all his rizzing, mewing, and mogging, the tax authorities have come knocking on Baby Gronk’s door. Oh no! They’re demanding that he pay a massive fanum tax, but the worst part is they haven’t told him how much the tax is. Instead, they gave him a riddle to solve. They gave him a monic polynomial \( p \) of degree 3 such that $$|p(1)| = |p(2)| = |p(3)| = |p(5)| = |p(6)| = |p(7)|$$ and told him that the fanum tax is equal to the value of \( |p(0)| \). Help Baby Gronk figure out how much fanum tax he has to pay!!! [/lang]