Neka su x1,x2,…,x100x_1, x_2, \ldots, x_{100}x1,x2,…,x100 realni brojevi za koje vrijedi
∣2xk−xk+1∣=xk+2za sve k∈{1,2,…,98},∣2x99−x100∣=x1,∣2x100−x1∣=x2.\begin{aligned} |2x_k - x_{k+1}| &= x_{k+2} \quad \text{za sve } k \in \{1, 2, \ldots, 98\}, \\ |2x_{99} - x_{100}| &= x_1, \\ |2x_{100} - x_1| &= x_2. \end{aligned}∣2xk−xk+1∣∣2x99−x100∣∣2x100−x1∣=xk+2za sve k∈{1,2,…,98},=x1,=x2.
Dokaži da je x1=x2=⋯=x100x_1 = x_2 = \cdots = x_{100}x1=x2=⋯=x100.