Mathematics — Unit 1 — Test 19

Eisenstein’s criterion with prime p proves irreducibility of x^5+10x^2+5 over Z when p=

Let I=(2,x)⊂Z[x]. Then

Which statement about the ideal I=(2,x)⊂Z[x] is correct?

Let R be a Euclidean domain. Which must be true?

In a UFD, the polynomial f(x)∈R[x] is primitive if

Gauss’s lemma says: For UFD R, if f,g∈R[x] are primitive, then

In a PID, any two elements a,b have a gcd d with

In Z, does the congruence 12x≡8 (mod 20) have solutions, and how many classes mod 20?

Chinese Remainder Theorem: Z/nZ ≅ Z/aZ × Z/bZ iff