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.

Statistics:

 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