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1. Let m be a positive integer. If a = b (mod m) and c= d (mod m), a) Prove a+c= b + d (mod m) b) Prove ac = bd (mod m)

1. Let m be a positive integer. If a = b (mod m) and c= d (mod m), a) Prove a+c= b + d (mod m) b) Prove ac = bd (mod m)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.2: Properties Of Division
Problem 50E
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1. Let m be a positive integer. If a = b (mod m) and c= d (mod m), a) Prove a + c = b + d (mod m) b) Prove ac = bd (mod m) 2. Find GCD and LCM of 256 and 162 using Prime Factorization. 3. Find GCD and LCM of 10! and 10³ using Prime Factorization. 4. x and y are two positive integers. (x,y) = 5, Icm (x,y) = 200 and 15, find x and y. gcd x - y =
Transcribed Image Text:1. Let m be a positive integer. If a = b (mod m) and c= d (mod m), a) Prove a + c = b + d (mod m) b) Prove ac = bd (mod m) 2. Find GCD and LCM of 256 and 162 using Prime Factorization. 3. Find GCD and LCM of 10! and 10³ using Prime Factorization. 4. x and y are two positive integers. (x,y) = 5, Icm (x,y) = 200 and 15, find x and y. gcd x - y =
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