query: Re: Find all primes $p$ such that $\phi(x)=x^{13}$ is a homomorphism $\Bbb Z/p\Bbb Z \rightarrow \Bbb Z/p\Bbb Z$.
positive_passages.docid: 144928
positive_passages.text: Find all primes $p$ such that $\phi(x)=x^{13}$ is a homomorphism $\Bbb Z/p\Bbb Z \rightarrow \Bbb Z/p\Bbb Z$.
negative_passages.docid: 31216
negative_passages.text: Is the image of $\Phi_n(x) \in \mathbb{Z}[x]$ in $\mathbb{F}_q[x]$ still a cyclotomic polynomial?
negative_passages.docid: 13764
negative_passages.text: Homomorphisms from $\mathbb{Z} \rightarrow S_3$.
negative_passages.docid: 27670
negative_passages.text: Group homomorphisms $\mathbb{Q}\to\mathbb{R}$
negative_passages.docid: 125582
negative_passages.text: Let $\phi:G_1\to G_2$ be a group homomorphism. Show $\phi(g^{-1})=(\phi(g))^{-1}$.
negative_passages.docid: 64025
negative_passages.text: Ring homomorphisms from $\Bbb Q$ into a ring
negative_passages.docid: 57732
negative_passages.text: Rings of fractions and homomorphisms
negative_passages.docid: 15000
negative_passages.text: Show that number of elements in $(Z/nZ)^*$ is $\phi (n)$
negative_passages.docid: 61334
negative_passages.text: Application of Main Homomorphism Theorem
negative_passages.docid: 97009
negative_passages.text: Image of ring homomorphism $\phi : \mathbb{Z}[t] \to \mathbb{Q}$?
negative_passages.docid: 159005
negative_passages.text: Finding all homomorphisms between two groups - couple of questions
negative_passages.docid: 88656
negative_passages.text: For $p$ prime, show that $\Phi_{p^n}(x) = 1 + x^{p^{n-1}} + x^{2p^{n-2}} + \dots +x^{(p-1)^{p^n-1}}$
negative_passages.docid: 120971
negative_passages.text: (Revised) Prove that $\phi$ is a group homomorphism and find the kernel.
negative_passages.docid: 3775
negative_passages.text: How many maps $\phi:\Bbb{N}\to\Bbb{N}$ are there with $\phi(ab) = \phi(a)+\phi(b)$?
negative_passages.docid: 123419
negative_passages.text: Abstract algebra: homomorphism and an element of a prime order
negative_passages.docid: 26661
negative_passages.text: Ring homomorphisms from $\mathbb{Z}_n$ to $\mathbb{Z}_m$
negative_passages.docid: 97258
negative_passages.text: Give $\ker(\phi)$ for $\phi: \mathbb{Z} \to \mathbb{Z_7}$ such that $\phi(1)=4$