2. Show that if a and b are positive integers and alb, then a < b. 3. Show that if a and b are integers such that alb, then ak|b* for every positive integer k. 4. Prove that for any integer a, 3 divides (a – 3)(a + 4)(a + 2).
2. Show that if a and b are positive integers and alb, then a < b. 3. Show that if a and b are integers such that alb, then ak|b* for every positive integer k. 4. Prove that for any integer a, 3 divides (a – 3)(a + 4)(a + 2).
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.4: Prime Factors And Greatest Common Divisor
Problem 28E: Let and be positive integers. If and is the least common multiple of and , prove that . Note...
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