. Suppose that p is a prime integer. (a) Show that if [x], [y] € Z and neither of which is [0], then [x] · [y] ‡ [0]. . (b) Show that for every [x] € Zp, [x] ‡ [0], there exists a [y] so that [x] · [y] = [1].

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 56E
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4. Suppose that p is a prime integer.
(a) Show that if [x], [y] ≤ Z₂ and neither of which is [0], then [x] · [y] ‡ [0].
(b) Show that for every [x] = Zp, [x] ‡ [0], there exists a [y] so that [x] · [y] = [1].
Transcribed Image Text:4. Suppose that p is a prime integer. (a) Show that if [x], [y] ≤ Z₂ and neither of which is [0], then [x] · [y] ‡ [0]. (b) Show that for every [x] = Zp, [x] ‡ [0], there exists a [y] so that [x] · [y] = [1].
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