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

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Problem A. 421. (February 2007)

A. 421. Find positive constants $\alpha$ and c such that

$\bigg| \sum_{k=1}^N \bigg\{\frac{k^2}{N}\bigg\} - \frac{N}{2} \bigg| < cN^{1-\alpha}$

holds for all positive integer N.

(5 pont)

Deadline expired on March 19, 2007.

3 students sent a solution.

4 points: Tomon István.

2 points: 2 students.