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Problem 3. Let a, b and n be positive integers. Prove that (a) gcd(a", br) = gcd(a, b)" and lcm(a", br) = lcm(a, b)"; (b) gcd (a • n, b. n) = gcd(a, b) · n and lcm(a · n, b⋅n) = lcm(a, b) · n;

Problem 3. Let a, b and n be positive integers. Prove that (a) gcd(a", br) = gcd(a, b)" and lcm(a", br) = lcm(a, b)"; (b) gcd (a • n, b. n) = gcd(a, b) · n and lcm(a · n, b⋅n) = lcm(a, b) · n;

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 3. Let a, b and n be positive integers. Prove that (a) gcd(a", br) = gcd(a, b)” and lcm(a^, b") = lcm(a, b)”; (b) gcd(a-n, b.n) = gcd(a, b) · n and lcm(an, b⋅ n) = lcm(a, b) . n;
Transcribed Image Text:Problem 3. Let a, b and n be positive integers. Prove that (a) gcd(a", br) = gcd(a, b)” and lcm(a^, b") = lcm(a, b)”; (b) gcd(a-n, b.n) = gcd(a, b) · n and lcm(an, b⋅ n) = lcm(a, b) . n;
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