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6. Let m, n EN with m, n > 2, and let a, b E Z. Prove that a = b (mod mn) implies a = b (mod m) and a = b (a) (mod n). (b) counterexample. Is the converse of part (a) true? If so, prove it. If not, give a

6. Let m, n EN with m, n > 2, and let a, b E Z. Prove that a = b (mod mn) implies a = b (mod m) and a = b (a) (mod n). (b) counterexample. Is the converse of part (a) true? If so, prove it. If not, give a

Algebra & Trigonometry with Analytic Geometry
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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6. Let m, n E N with m, n > 2, and let a, b E Z. Prove that a = b (mod mn) implies a = b (mod m) and a = b (a) (mod n). (b) counterexample. Is the converse of part (a) true? If so, prove it. If not, give a
Transcribed Image Text:6. Let m, n E N with m, n > 2, and let a, b E Z. Prove that a = b (mod mn) implies a = b (mod m) and a = b (a) (mod n). (b) counterexample. Is the converse of part (a) true? If so, prove it. If not, give a
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