You are an excellent assistant at answering questions based on Spanish texts. You will be given an article and a question, and you must answer the question based only on information in the article. The response should be extracted from the context verbatim.

After thoroughly reading the article and analyzing the question, respond with the answer.

Title:
Prime_number

Context:
Prime ideals are the points of algebro-geometric objects, via the notion of the spectrum of a ring. Arithmetic geometry also benefits from this notion, and many concepts exist in both geometry and number theory. For example, factorization or ramification of prime ideals when lifted to an extension field, a basic problem of algebraic number theory, bears some resemblance with ramification in geometry. Such ramification questions occur even in number-theoretic questions solely concerned with integers. For example, prime ideals in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns the solvability of quadratic equations

Question:
In what type of ring can prime ideals be used for validating quadratic reciprocity?

ring of integers of quadratic number fields