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donjar

Fungsi 4 variabel linear lucu

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Cari semua fungsi $f$ yang memetakan semua bilangan real ke bilangan real nonnegatif, sehingga untuk setiap $a, b, c, d \in \mathbb{R}$ yang memenuhi $ab + bc + cd = 0$, dipunyai \[ f(a - b) + f(c - d) = f(a) + f(b + c) + f(d).\]

 

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Korea NMO Final Round 2013 no. 2

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