List questions from multiplicative-function

Published on 14 Jan 2024 - 2:15

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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

Published on 16 Jan 2024 - 1:56

33

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Average of Multiplicative Function

Published on 07 Feb 2024 - 21:17

146

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Probability that one random number among many has a unique prime factor

Published on 13 Feb 2024 - 14:27

109

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Why is 15 + 15 different from 15 * 2?

Published on 20 Jan 2015 - 16:01

465

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Identity in Number Theory Paper

Published on 23 Jan 2015 - 0:41

3.8k

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Grade School Multiplication Algorithm for Binary Numbers explanation

Published on 24 Jan 2015 - 21:00

352

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Why is this expression returning NaN?

Published on 25 Feb 2015 - 11:58

262

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Möbius function on a finite poset (X, $\leq$)

Published on 02 Mar 2015 - 7:08

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

Published on 09 Mar 2015 - 5:08

808

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

Published on 19 Mar 2015 - 1:30

699

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formula for the number of perfect squares mod $N$

Published on 28 Mar 2015 - 16:51

345

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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?

Published on 02 Apr 2015 - 18:34

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

Published on 15 Apr 2015 - 4:24

233

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Proving that a summation is multiplicative

Published on 25 Apr 2015 - 21:10

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Summation notation over divisors confusion

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

Average of Multiplicative Function

Probability that one random number among many has a unique prime factor

Why is 15 + 15 different from 15 * 2?

Identity in Number Theory Paper

Grade School Multiplication Algorithm for Binary Numbers explanation

Why is this expression returning NaN?

Möbius function on a finite poset (X, $\leq$)

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

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

formula for the number of perfect squares mod $N$

If a function $f$ is multiplicative, how do I show that $\sum_{d\mid n} \mu(n/d) f(d)$ is also multiplicative?

Euler's Totient function $\forall n\ge3$, if $(\frac{\varphi(n)}{2}+1)\ \mid\ n\ $ then $\frac{\varphi(n)}{2}+1$ is prime

Proving that a summation is multiplicative

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