Problem

Source: IFYM - XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade, 4th round p4

Tags: algebra



Let $n$ be a natural number. To prove that the value of the expression $$\prod^n_{i=0}\frac{x^{n-1}_i}{\prod_{j \ne i}(x_i - x_j)}$$does not depend on the choice of the different real numbers $x_0, x_1, ... , x_n$.