Problem A. 587. (April 2013)
A. 587. Find all positive integers n for which there exists a sequence a1<a2<...<an of positive integers with the property that the sums ai+aj with 1i<jn are distinct and among them each modulo 4 residue occurs the same number of times.
(Proposed by Ilya Bogdanov, Moscow)
Deadline expired on May 10, 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.