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Summation notation over divisors confusion

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#number-theory #elementary-number-theory #summation #notation #multiplicative-function
74
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Let $F: \mathbb R^n \to \mathbb R^m$ be smooth and such that for all $a \in \mathbb R$, $x \in \mathbb R^n$, $F(ax) = aF(x)$. Prove $F$ is linear

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#linear-algebra #smooth-functions #multiplicative-function
36
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Average of Multiplicative Function

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#multiplicative-function
149
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Probability that one random number among many has a unique prime factor

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#probability #number-theory #prime-numbers #analytic-number-theory #multiplicative-function
112
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Why is 15 + 15 different from 15 * 2?

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#multiplicative-function
468
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Identity in Number Theory Paper

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#number-theory #summation #products #multiplicative-function
3.8k
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Grade School Multiplication Algorithm for Binary Numbers explanation

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#algorithms #binary #multiplicative-function
355
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Why is this expression returning NaN?

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#multiplicative-function
263
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Möbius function on a finite poset (X, $\leq$)

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#combinatorics #number-theory #multiplicative-function #mobius-function
2.4k
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new addition and new multiplication x ⊕ y = x + y − 1, x ⊗ y = x + y − xy on set Z, prove the set Z equipped with these 2 new operation

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#ring-theory #multiplicative-function
810
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Convolution identity involving the Möbius function $\sum_{d|n,d>0} |\mu(d)| = 2^{\omega(n)}$

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#number-theory #arithmetic-functions #multiplicative-function #mobius-function #dirichlet-convolution
703
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formula for the number of perfect squares mod $N$

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#elementary-number-theory #multiplicative-function #oeis
348
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If a function $f$ is multiplicative, how do I show that $\sum_{d\mid n} \mu(n/d) f(d)$ is also multiplicative?

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#elementary-number-theory #multiplicative-function
1k
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Euler's Totient function $\forall n\ge3$, if $(\frac{\varphi(n)}{2}+1)\ \mid\ n\ $ then $\frac{\varphi(n)}{2}+1$ is prime

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#elementary-number-theory #prime-numbers #totient-function #conjectures #multiplicative-function
236
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Proving that a summation is multiplicative

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#number-theory #summation #multiplicative-function

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