23 22. Prove that f(n) = [√n]—[√n − 1] is a multiplicative function, but it is not completelymultiplicative.23. Let f be a multiplicative function. Examine whether F(n) = [Idn f(d) is multiplicativeor not.

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Let f be a multiplicative function. Examine whether F(n) = [Idn f(d) is multiplicative

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 30EQ

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Question

22. Prove that f(n) = [√n]—[√n − 1] is a multiplicative function, but it is not completely
multiplicative.
23. Let f be a multiplicative function. Examine whether F(n) = [Idn f(d) is multiplicative
or not.

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