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

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Problem A. 520. (November 2010)

A. 520. Is there any infinite sequence a₁,a₂,... of nonnegative numbers for which $\sum_{n=1}^\infty a_n^2$ is finite and

$\sum_{n=1}^\infty \bigg(\sum_{k=1}^\infty\frac{a_{kn}}{k}\bigg)^{2} = \infty?$

(Miklós Schweitzer Competition, 2010)

(5 pont)

Deadline expired on December 10, 2010.

4 students sent a solution.

5 points: Nagy 235 János.

0 point: 3 students.