MathDB

1

Part of 2005 Serbia Team Selection Test

Problems(2)

A trig one with absurb

Source: Serbia TST 2005

11/28/2005
Prove that there is n rational number rr such that cosrπ=35cosr\pi=\frac{3}{5}
trigonometrycomplex numbersirrational numberalgebra proposedalgebra
serbia BMO

Source: serbia team selection test for balkan mo 2005

5/5/2017
problem 1 :A sequence is defined byx1=1,x2=4 x_1 = 1, x_2 = 4 and xn+2=4xn+1−xn x_{n+2} = 4x_{n+1} -x_n for n≥1n \geq 1. Find all natural numbers mm such that the number 3xn2+m3x_n^2 + m is a perfect square for all natural numbers nn
algebra