Suppose that p and q are integers with 0 < p, 0
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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Question
![Suppose that p and q are integers with 0 < p, 0 <p+q, and the greatest common divisor of p
and q is 1. For a positive integer k, let P(k) be the lowest common multiple of p+q, p+2q,p+
3q,,p+kq.
Prove that
1
P(k) 1
k
lim log
k→∞
=
Σ
o(1) m
1<m<l
where
(a) (1) is the number of integers between 1 and 1 that are relatively prime to 1 and
(b) the greatest common divisor of m and 1 is 1 for all m.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F271092a1-6334-46e1-88cf-0748a7aac0cc%2F74315dc3-368a-48c0-81c2-6774fe302c2b%2Fvogn76p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose that p and q are integers with 0 < p, 0 <p+q, and the greatest common divisor of p
and q is 1. For a positive integer k, let P(k) be the lowest common multiple of p+q, p+2q,p+
3q,,p+kq.
Prove that
1
P(k) 1
k
lim log
k→∞
=
Σ
o(1) m
1<m<l
where
(a) (1) is the number of integers between 1 and 1 that are relatively prime to 1 and
(b) the greatest common divisor of m and 1 is 1 for all m.
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