Mathematical and Physical Journal
for High Schools
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Problem B. 4801. (May 2016)

B. 4801. Define the sequence \(\displaystyle f_n\) of functions by the following recurrence relation:

\(\displaystyle f_0(x) = f_1(x) = 1, \mathrm{~and ~for ~} n\ge 2 \quad f_n(x) = f_{n-1}(x) \cdot 2\cos(2x) - f_{n-2}(x). \)

Determine the number of roots of \(\displaystyle f_n(x)\) in the interval \(\displaystyle [0,\pi]\).

Proposed by L. Bodnár, Budapest

(5 pont)

Deadline expired on June 10, 2016.


Statistics:

25 students sent a solution.
5 points:Andó Angelika, Baran Zsuzsanna, Fajszi Bulcsú, Gáspár Attila, Horváth András János, Imolay András, Kocsis Júlia, Lajkó Kálmán, Matolcsi Dávid, Németh 123 Balázs, Polgár Márton, Tóth Viktor, Váli Benedek.
4 points:Jakus Balázs István, Kerekes Anna, Nagy Dávid Paszkál.
3 points:4 students.
2 points:1 student.
1 point:3 students.
0 point:1 student.

Problems in Mathematics of KöMaL, May 2016