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Part of 1994 Hungary-Israel Binational

Problems(1)

Hungary-Israel Binational 1994_2

Source:

10/29/2008
Let a1 a_1, … \ldots, ak a_k, a_{k\plus{}1}, … \ldots, an a_n be n n positive numbers (k<n k<n). Suppose that the values of a_{k\plus{}1}, a_{k\plus{}2}, … \ldots, an a_n are fixed. Choose the values of a1 a_1, a2 a_2, … \ldots, ak a_k that minimize the sum ∑i,j,i≠jaiaj \sum_{i, j, i\neq j}\frac{a_i}{a_j}
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