Let x, y ∈Z. Prove that if x≡1(mod 5) and y ≡2(mod5 ), then x^2-y^2≡0(mod 5). Give 2 examples to show that this scenario either does or does not work. Give the proof with an explanation to each step.
Let x, y ∈Z. Prove that if x≡1(mod 5) and y ≡2(mod5 ), then x^2-y^2≡0(mod 5). Give 2 examples to show that this scenario either does or does not work. Give the proof with an explanation to each step.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 16E
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Let x, y ∈Z. Prove that if x≡1(mod 5) and y ≡2(mod5 ), then x^2-y^2≡0(mod 5).
Give 2 examples to show that this scenario either does or does not work.
Give the proof with an explanation to each step.
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