The conversation between human and AI assistant.
How do I show that polynomial [math]p(x)=\frac {p(x+1) + p (x-1)}{2}[/math] has degree atmost 1?
I see. So, what is the next step?
We can substitute these expressions into [math]p(x)=\frac{1}{2}p(x+1) + \frac{1}{2}p(x-1)[/math], and simplify as [math]p(x)=\frac{1}{2}(x+1)^n + \frac{1}{2}(x-1)^n[/math].