Problem

Source: VII International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

Tags: algebra, Polynomials



Find all polynomials $P\in \mathbb{Q}[x]$, which satisfy the following equation: $P^2 (n)+\frac{1}{4}=P(n^2+\frac{1}{4})$ for $\forall$ $n\in \mathbb{N}$.