Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation

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Problem A. 374. (May 2005)

A. 374. The real numbers x₁ $\ge$ x₂ $\ge$ ... $\ge$ x_n>0 and y₁ $\ge$ y₂ $\ge$ ... $\ge$ y_n>0 satisfy

$\prod_{i=1}^kx_i\ge\prod_{i=1}^ky_i.$

for all 0<k $\le$ n. Prove that

$\sum_{i=1}^nx_i\ge\sum_{i=1}^ny_i.$

(5 pont)

Deadline expired on June 15, 2005.

2 students sent a solution.

5 points: Paulin Roland, Strenner Balázs.

2 students sent a solution.
5 points:	Paulin Roland, Strenner Balázs.