Mathematical and Physical Journal
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Problem A. 374. (May 2005)

A. 374. The real numbers x1\gex2\ge...\gexn>0 and y1\gey2\ge...\geyn>0 satisfy


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

for all 0<k\len. Prove that


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

(5 pont)

Deadline expired on June 15, 2005.


Statistics:

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

Problems in Mathematics of KöMaL, May 2005