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akun

APMO 2017 No 5 - Pasangan Istimewa

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Misalkan \(n\) adalah bilangan bulat positif. Sepasang \(n\)-tupel \((a_1,\cdots ,a_n)\) dan \((b_1,\cdots ,b_n)\) dengan anggota bilangan bulat disebut pasangan istimewa jika

\(\left | a_1b_1+\cdots +a_nb_n \right |\leq 1.\)

Tentukan jumlah maksimum dari \(n\)-tupel berbeda dengan anggota bilangan bulat dimana sebarang dua dari mereka membentuk pasangan istimewa.

 

Edited by akun
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