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(b) Show that if gcd(m, n) = 1, then σ₁ (mn) = σt(m)ot(n). In other words, show that function. Is this formula still true if m and n are not relatively Ot is a multiplicative prime?

(b) Show that if gcd(m, n) = 1, then σ₁ (mn) = σt(m)ot(n). In other words, show that function. Is this formula still true if m and n are not relatively Ot is a multiplicative prime?

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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26.3. Let d₁, d2,..., dr be the numbers that divide n, including 1 and n. The t-power sigma function ot(n) is equal to the sum of the tth powers of the divisors of n, ot(n) = ₁ + d₂ + ... + dt. For example, 02 (10) = 1² +2²+5² +10² = 130. Of course, σ₁ (n) is just our old friend, the sigma function o(n).
Transcribed Image Text:26.3. Let d₁, d2,..., dr be the numbers that divide n, including 1 and n. The t-power sigma function ot(n) is equal to the sum of the tth powers of the divisors of n, ot(n) = ₁ + d₂ + ... + dt. For example, 02 (10) = 1² +2²+5² +10² = 130. Of course, σ₁ (n) is just our old friend, the sigma function o(n).
(b) Show that if gcd(m, n) = 1, then σt (mn) = 0+ (m)ot (n). In other words, show that function. Is this formula still true if m and n are not relatively ot is a multiplicative prime?
Transcribed Image Text:(b) Show that if gcd(m, n) = 1, then σt (mn) = 0+ (m)ot (n). In other words, show that function. Is this formula still true if m and n are not relatively ot is a multiplicative prime?
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