### Questions (36)

 3 Distributing $3$ blue and $4$ green and $9$ red balls into $3$ distinct urns 3 prove $\left(3, 1+\sqrt{-5}\right)$ is prime ideal of $\mathbb{Z}\left[\sqrt{-5}\right]$ 3 If $P$ is an invertible linear operator on a finite dimensional vector space over a finite field, then there is some $n>0$ such that $P^n=I$ 2 The degree of an irreducible factor of a composite polynomial 2 Doubt from Spivak's proof of inverse function theorem.

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### Tags (35)

 0 group-theory × 9 0 ring-theory × 3 0 real-analysis × 8 0 linear-algebra × 3 0 multivariable-calculus × 6 0 abelian-groups × 3 0 maximal-and-prime-ideals × 4 0 finite-groups × 2 0 polynomial-rings × 3 0 unique-factorization-domains × 2

### Bookmarks (3)

 10 Cardinality of $A=\{f: \mathbb R \to \mathbb R , f \text{ is continuous and} f(\mathbb Q) \subset \mathbb Q\}$ 4 Cardinality of this set: $A=\{f: \mathbb{R} \rightarrow \mathbb{R} \text{ continuous} : f(\mathbb{Q})\subseteq\mathbb{Q}\}$ 3 Calculating a multivariable limit.

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