Mathematical and Physical Journal
for High Schools
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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.

Problems in Mathematics of KöMaL, February 2007