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Let 01(x) = * 0(t) dt, for x > 1, where 0 is Chebyshev's function. Let A1(n) = log n if n is prime, and A₁(n) = 0 otherwise. Prove that 01(x) = (x − n) A1(n), n

Let 01(x) = * 0(t) dt, for x > 1, where 0 is Chebyshev's function. Let A1(n) = log n if n is prime, and A₁(n) = 0 otherwise. Prove that 01(x) = (x − n) A1(n), n

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 9T
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Let 01(x) = * 0(t) dt, for x > 1, where 0 is Chebyshev's function. Let A1(n) = log n if n is prime, and A₁(n) = 0 otherwise. Prove that 01(x) = (x − n) A1(n), n<x -
Transcribed Image Text:Let 01(x) = * 0(t) dt, for x > 1, where 0 is Chebyshev's function. Let A1(n) = log n if n is prime, and A₁(n) = 0 otherwise. Prove that 01(x) = (x − n) A1(n), n<x -
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