TST TAJIKISTAN 2018 Day 3
Source:
July 10, 2018
TajikistanIMO TST 2018Problem 2
Problem Statement
Problem 8. For every non-negative integer n, define an n-variable function K_n (x_1,x_2,…,x_n ) as follows:
K_0=1
K_1 (x_1 )=〖x_1〗^2
K_(n+2) (x_1,x_2,…,x_(n+2) )=〖x_(n+2)〗^2.K_(n+1) (x_1,x_2,…,x_(n+1) )+(x_(n+2)+x_(n+1))K_n (x_1,x_2,…,x_n )
Prove that:
K_n (x_1,x_2,…,x_n )=K_n (x_n,…〖,x〗_2,x_1 )