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Example on Euler Totient function

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#number-theory #divisibility #totient-function #multiplicative-function
66
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Modular Multiplicative inverse of exact multiples

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#modular-arithmetic #multiplicative-function
1k
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show that $ \sum_{p \leq x} \log p \big( \log x - \log p\big) = O(x) $

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#prime-numbers #analytic-number-theory #multiplicative-function #mobius-inversion
839
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Multiplicative Inverse using Fermats theorm

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#multiplicative-function
194
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Dirichlet character modulo $k$

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#number-theory #analytic-number-theory #multiplicative-function
142
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Closed form for $\sum\limits_{d|n}\sigma(d)$?

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#number-theory #divisor-sum #arithmetic-functions #multiplicative-function #dirichlet-convolution
702
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Dirichlet series associated to squared Möbius

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#analytic-number-theory #riemann-zeta #dirichlet-series #multiplicative-function #mobius-function
940
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Composition of multiplicative functions which is not multiplicative

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#elementary-number-theory #examples-counterexamples #function-and-relation-composition #multiplicative-function
2k
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Showing $\sum_{d\mid n} \mu(d)\tau(n/d)=1$ and $\sum_{d\mid n} \mu(d)\tau(d)=(-1)^r$

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#number-theory #mobius-function #multiplicative-function #divisor-counting-function #mobius-inversion
26
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Relation for multiplicative functions

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#number-theory #convolution #multiplicative-function
1.7k
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Prove that function is multiplicative

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#multiplicative-function
721
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If $F$ is multiplicative, then show that $f$ is multiplicative (without the Mobius inversion formula)

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#number-theory #multiplicative-function
421
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The group of number theoretic functions

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#group-theory #number-theory #proof-explanation #multiplicative-function
439
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Is every jordan homomorphism a ring homomorphism

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#functional-analysis #banach-algebras #multiplicative-function #ring-homomorphism
165
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Can $\sigma(p^k)=2^n$ for some $k>1$?

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#number-theory #prime-numbers #diophantine-equations #divisor-sum #multiplicative-function

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