Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem A. 653. (November 2015)

A. 653. Let \(\displaystyle n\ge2\) be an integer. Prove that there exist integers \(\displaystyle a_1,\dots,a_{n-1}\) such that \(\displaystyle a_1 \arctg 1 + a_2 \arctg 2 +\ldots+ a_{n-1}\arctg(n-1) = \arctg n\) if and only if \(\displaystyle n^2+1\) divides \(\displaystyle (1^2+1)(2^2+1)\ldots\big((n-1)^2+1\big)\).

Based on a problem of IMC 2015, Blagoevgrad

(5 pont)

Deadline expired on December 10, 2015.


7 students sent a solution.
5 points:Gáspár Attila, Lajkó Kálmán, Williams Kada.
4 points:Szabó 789 Barnabás.
2 points:2 students.
1 point:1 student.

Problems in Mathematics of KöMaL, November 2015