*The Princeton Companion to Mathematics* mentions that polynomials (for instance, ones with rational coefficients) share similarities with integers, thus leading to the idea of a general structure of the *Euclidean domain*. It isn't obvious to me how this is the case. Could you provide a palatable explanation?

# [Math] Simply put, what are the similarities between integers and polynomials

number theorypolynomials

## Best Answer

absolute value of integer <-> degree of polynomial

positive integer <-> monic polynomial

+/- 1 <-> constant polynomial

prime integer <-> irreducible polynomial

With these correspondences, there are many identical notions and theorems, like the division algorithm, unique prime factorization, principal ideals, LCM, GCD, ...