P3. (3+5 points) Let k be any natural number. (a) Prove that for every positive integer n, we have σk(n) = σ−k(n)n k . Conclude

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3 years ago

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P3. (3+5 points) Let k be any natural number. (a) Prove that for every positive integer n, we have σk(n) = σ−k(n)n k . Conclude

that n is a perfect number exactly when σ−1(n) = 2. (b) Prove that for all positive integers n, we have σ1(n) ≤ n log(n + 1) + γn, where γ is Euler’s constant defined in class. (In this course, log x = loge x denotes the natural logarithm). g

Mathematics

1 answer:

Mrac [35] · Answer 1 · 2022-08-22T10:59:56+03:00

Mrac [35]3 years ago

8 0

Answer:

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Step-by-step explanation:

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