Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation

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Problem A. 587. (April 2013)

A. 587. Find all positive integers n for which there exists a sequence a₁<a₂<...<a_n of positive integers with the property that the sums a_i+a_j with 1 $\le$ i<j $\le$ n are distinct and among them each modulo 4 residue occurs the same number of times.

(Proposed by Ilya Bogdanov, Moscow)

(5 pont)

Deadline expired on May 10, 2013.

Statistics:

9 students sent a solution.

5 points: Ágoston Péter, Janzer Olivér, Maga Balázs, Szabó 789 Barnabás, Szabó 928 Attila, Török 928 Mihály, Williams Kada.

4 points: Herczeg József.

3 points: 1 student.

Problems in Mathematics of KöMaL, April 2013

9 students sent a solution.
5 points:	Ágoston Péter, Janzer Olivér, Maga Balázs, Szabó 789 Barnabás, Szabó 928 Attila, Török 928 Mihály, Williams Kada.
4 points:	Herczeg József.
3 points:	1 student.