2

Part of 2006 Regional Competition For Advanced Students

Problems(1)

37th Austrian Mathematical Olympiad 2006

Source: round1, problem2 - systems of equations

n>1

be a positive integer an

a

a real number. Determine all real solutions

(x_1,x_2,\dots,x_n)

to following system of equations: x_1\plus{}ax_2\equal{}0 x_2\plus{}a^2x_3\equal{}0 … x_k\plus{}a^kx_{k\plus{}1}\equal{}0 … x_n\plus{}a^nx_1\equal{}0

algebrasystem of equationsalgebra unsolved