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;

To prove the given statements, we will use the following properties of the greatest common divisor…

Answered: Problem 3. Let a, b and n be positive…

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(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; . .