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Misalkan $a_1, a_2, \ldots, a_n$ merupakan $n$ bilangan bulat yang berbeda. Tentukan semua polinom dengan koefisien bilangan bulat $f(x)$ sehingga $$\sum^n_{i=1} \frac{f(a_i)}{\displaystyle \prod_{j \neq i} (a_i - a_j)}$$ merupakan bilangan bulat.


 


by Aleams Barra, Tes 2 no. 4 Pelatnas 3 IMO 2014


 


p.s. Ada baiknya Anda mencoba soal ini sebelum membuka spoiler di bawah:



Matriks Vandermonde :D



Edited by donjar

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