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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

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 3TFE: Label each of the following statements as either true or false. a2b2(modn) and implies ab(modn) or...
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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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