Essentially they are both integral domains: https://en.wikipedia.org/wiki/Integral_domain https://en.wikipedia.org/wiki/Integral_domain The space of integers a

Essentially they are both integral domains: https://en.wikipedia.org/wiki/Integral_domain https://en.wikipedia.org/wiki/Integral_domain The space of integers and polynomials have a lot of things in common. They have well-defined addition and multiplication operations, they have a zero value and a one value (for integers it is literally 0 and 1, for polynomials it's the constant function returning 0 and 1, respectively) that obey the usual laws (x + 0 = 0, x1 = x, x0=0, etc). They also both have no zero divisors, i.e. if a*b = 0, then either a=0 or b=0. From just those basic notions you can define divisibility and factorization in a way that applies to both polynomials and integers. In a very deep way, any property or concept you define on the integers can (often, but of course there are exceptions) be extended to apply to polynomials. There might be some category-theoretic way to formally state that relationship, I'm not sure.