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If I recall correctly, Andreescu & Andrica attributed the olympiad problem which prompted this question by S. Pek to the Russian magazine Kvant. Does anybody here know if the problem actually appeared in the pages of Kvant once?

Hope this question of mine doesn't get closed... I dared to ask it here because I believe that several MO users were avid readers of Kvant back in the day.

Thanks in advance for your attention!

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    $\begingroup$ Looks like a perfectly legitimate question to me, fitting perfectly the reference request tag. Cannot see why it should be closed. $\endgroup$
    – Seva
    Commented Nov 16, 2016 at 8:07

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Yes, it is problem M618a), published in No. 4, 1980. Part b) claimed that for every $\alpha>0$ there exist infinitely many $n$ with $n^2+1\mid [\alpha n]!$. The problem is attributed to A. Sivatsky (who was a 10th grade student at that time).

The solution is in No. 2, 1981. Also, this problem is discussed in an article by V. Senderov and A. Spivak in No. 4, 2002. If you need, I may find a cite to the electronic versions of all these.

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