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How to prove if an arithmetic function is multiplicative?

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#prime-numbers #multiplicative-function
763
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A unsolved puzzle from Number Theory/ Functional inequalities

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#number-theory #inequality #functional-equations #functional-inequalities #multiplicative-function
1.3k
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The multiplicative property of cofactor matrices

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#linear-algebra #multiplicative-function
49
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An inequality involving Möbius function

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#elementary-number-theory #inequality #summation #arithmetic-functions #multiplicative-function
846
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Prove $\sum_{k\mid n}{\mu(k)d(k)}=(-1)^{\omega{(n)}}$

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#number-theory #multiplicative-function #divisor-counting-function #mobius-inversion #dirichlet-convolution
980
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suppose $\omega(n)$ denote the number of distinct prime factors of n

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#elementary-number-theory #multiplicative-function
2.3k
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Prove that the Möbius function is multiplicative

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#elementary-number-theory #arithmetic-functions #multiplicative-function
2.7k
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For any positive integer $n$, show that $\sum_{d|n}\sigma(d) = \sum_{d|n}(n/d)\tau(d)$

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#elementary-number-theory #summation #divisor-sum #multiplicative-function #divisor-counting-function
2.1k
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Prove that $\sum \limits_{d|n}(n/d)\sigma(d) = \sum \limits_{d|n}d\tau(d)$

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#elementary-number-theory #summation #divisor-sum #multiplicative-function #divisor-counting-function
172
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Is the totient function $\varphi$ invertible?

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#elementary-number-theory #totient-function #arithmetic-functions #multiplicative-function
336
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Show that the phi function is multiplicative $\phi(mn) = \phi(m)\phi(n)$

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#elementary-number-theory #totient-function #multiplicative-function
43
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How to show that

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#elementary-number-theory #multiplicative-function
769
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Euler-Totient Multiplicative

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#totient-function #chinese-remainder-theorem #multiplicative-function
35
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Multiplying fractions with an x value

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#multiplicative-function
61
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Simple act practice test problem

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#multiplicative-function

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