# How to construct a field with 25 elements of a given polynomial? [duplicate]

Let us say that the polynomial is $$x^2 + 5$$ and the field is $$\mathbb F_{25}$$. Hereby $$ax+b$$ denotes any element of $$\mathbb F_{25}$$ with both $$a$$ and $$b$$ in the field $$\mathbb F_5$$.

Hint: Try $$x^2-a$$ where $$a$$ is not a square mod $$5$$.