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IMO 2012 NO 4

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Cari semua fungsi $f : \mathbb{Z} \rightarrow \mathbb{Z}$ sehingga, untuk semua bilangan bulat $a$, $b$, $c$ yang memenuhi $a+b+c=0$, persamaan ini berlaku:


$f(a)^2+f(b)^2+f(c)^2 = 2f(a)f(b) + 2f(b)f(c) + 2f(c)f(a)$


(Disini $\mathbb{Z}$ menotasikan himpunan bilangan bulat.)

Edited by Zekrom

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