Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
Already signed up?
New to KöMaL?

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