Problem B. 4775. (February 2016)

B. 4775. Find those pairs \(\displaystyle (n,k)\) of positive integers for which

\(\displaystyle \sum_{i=1}^{2k+1} {(-1)}^{i-1} a_{i}^{n}\ge \bigg(\sum_{i=1}^{2k+1} {(-1)}^{i-1} a_{i}\bigg)^{\!\!n} \)

for all real numbers \(\displaystyle a_1\ge a_2\ge \dots \ge a_{2k+1}\ge 0\).

Proposed by Á. Somogyi, Budapest

(6 pont)

Deadline expired on March 10, 2016.

Statistics:

29 students sent a solution.
6 points:	Baran Zsuzsanna, Besenyi Tibor, Bodolai Előd, Borbényi Márton, Bukva Balázs, Döbröntei Dávid Bence, Gáspár Attila, Glasznova Maja, Hansel Soma, Harsányi Benedek, Horváth András János, Imolay András, Klász Viktória, Kőrösi Ákos, Lajkó Kálmán, Matolcsi Dávid, Németh 123 Balázs, Tóth Viktor, Váli Benedek.
5 points:	Busa 423 Máté, Nagy Dávid Paszkál, Souly Alexandra.
3 points:	1 student.
1 point:	4 students.
0 point:	1 student.
Unfair, not evaluated:	1 solutions.

Problems in Mathematics of KöMaL, February 2016