Question

(i) Show that a non-zero polynomial in ??[?]Zp[x] has exactly ?−1p−1 associates.

(ii) Let ?R be a field, 0≠?(?),?(?)∈?[?]0≠a(x),b(x)∈R[x]. Prove that ?(?)a(x) ?(?)b(x) are associates of each other if and only if ?(?)∣?(?)a(x)∣b(x)and ?(?)∣?(?)b(x)∣a(x).

Q5 (4 points) (i) Show that a non-zero polynomial in Zp[x] has exactly p - 1 associates. a(x), b(x) E R[x]. Prove that a(x) b

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(i) Show that a non-zero polynomial in ??[?]Zp[x] has exactly ?−1p−1 associates. (ii) Let ?R be...
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