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Problem 3. Let a, b and n be positive integers. Prove that (a) gcd(an, b″) = gcd(a, b)” and lcm(a”, b″) = 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(an, b″) = gcd(a, b)” and lcm(a”, b″) = 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^, bn) = gcd(a, b)” and lcm(a^, b") = lcm(a, b)”; (b) gcd(a-n, b.n) = gcd(a, b) · n and lcm(a · n, b⋅ n) = lcm(a, b) · n;
Transcribed Image Text:Problem 3. Let a, b and n be positive integers. Prove that (a) gcd(a^, bn) = gcd(a, b)” and lcm(a^, b") = lcm(a, b)”; (b) gcd(a-n, b.n) = gcd(a, b) · n and lcm(a · n, b⋅ n) = lcm(a, b) · n;
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