. Consider the statement: Let A, B ∈ Z. If 6|A and 10|B, then 4|(A2 + B2). (a) Prove the statement. What kind of proof are you using? (b) State the converse. (c) Is the converse true or not? If true, then prove it. If false, give a counterexample

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 90E
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5. Consider the statement: Let A, B ∈ Z. If 6|A and 10|B, then 4|(A2 + B2).

(a) Prove the statement. What kind of proof are you using?

(b) State the converse.

(c) Is the converse true or not? If true, then prove it. If false, give a counterexample

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