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