MathDB

4

Part of 2016 Azerbaijan BMO TST

Problems(3)

Functional Equation

Source:

2/19/2016
Find all functions f:N→Nf:\mathbb{N}\to\mathbb{N} such that f(f(n))=n+2015f(f(n))=n+2015 where n∈N.n\in \mathbb{N}.
functionalgebrafunctional equation
Balkan TSTp3.4

Source: Azerbaijan Balkan TST 2016 no 3

10/20/2016
For all numbers n≥1n\ge 1 does there exist infinite positive numbers sequence x1,x2,...,xnx_1,x_2,...,x_n such that xn+2=xn+1−xnx_{n+2}=\sqrt{x_{n+1}}-\sqrt{x_n}
algebra
Balkan TSTp4.4

Source: Azerbaijan Balkan TST 2016 no 4

10/20/2016
Let ABCABC be an acute triangle and let MM be the midpoint of ACAC. A circle ω\omega passing through BB and MM meets the sides ABAB and BCBC at points PP and QQ respectively. Let TT be the point such that BPTQBPTQ is a parallelogram. Suppose that TT lies on the circumcircle of ABCABC. Determine all possible values of BTBM\frac{BT}{BM}.
geometry