# Tagged Questions

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### I managed to prove this … Can it be used for anything?

I managed to show: $$x = \sum_{k=1}^{\infty} \sum_{r=1}^{\infty} \mu (k) x^{kr}$$ where $\mu(k)$ is mobius function and $x$ belongs from (-1,1) Can this be used for anything?
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### Determing sequence from its Dirichlet series

Suppose I know the Dirchlet series $$\sum_{n=1}^{\infty} \frac{f(n)}{n^s} = \frac{\zeta(s)}{\zeta(3s)},$$ where $\zeta(s)$ is the usual Riemann zeta function. My question is - is there a way to ...
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### Exponential generating function for number of 10 length sequences built from the alphabet, with some restrictions

I've got the following homework question. If anybody could possibly point me in the right direction, that would be great: Suppose X is a sequence with 10 terms built from 26 letters {a, b, c, ..., ...
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### Discrete math: probability of picking certain hands with a preset condition

In 5-card draw poker, a player receives an initial hand of 5 cards, and is then allowed to replace up to three of her cards with the remaining cards in the deck. (b) Suppose that, among the initial 5 ...
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### Count the divisors of n with particular property

Take $n = \prod_{i=1}^r {p_i}^{\alpha_i}$, where each $p_i$ is a prime and $\alpha_i\geq 1$. How many divisors of $n$, not equal to $n$, contain at least one $p_i$ with the corresponding multiplicity ...
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### How to find $\sum_{d\mid n}(w(d)w(\frac{n}{d}))$?

i) $w(n)$ is the prime divisor count function. For example $w(6)=2$ ii) Let prime factorization of $n=p_{1}^{a_{1}}p_{2}^{a_{2}}.....p_{w(n)}^{a_{w(n)}}$ iii) Lets define this function. ...
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### Different values of $x$ and $y$ between $\sqrt{39}$ and $\sqrt{224}$

If $x$ and $y$ are whole numbers between $\sqrt{39}$ and $\sqrt{224}$, then how many different values can $x$ + $y$ have? OK, first I found that the set numbers are: $$7, 8 ,9 ,10 ,11 ,12, 13,14$$ ...
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### question on combinatorics and number theory

We have an equation as: $a\times b < n$ where $n$ is any positive integer. Now my question is how many pairs of positive integers $(a,b)$ can be found to satisfy the equation. For example, ...
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### Does Bezout's lemma imply you can generate all integers from two co-prime integers?

Does Bezout's lemma imply that: $x\mathbb{Z} + y\mathbb{Z} = \mathbb{Z}$? if $x\in\mathbb{Z}$, $y\in\mathbb{Z}$, $x\neq 0$ and $y\neq0$ and gcd$(x,y)=1$ ($x$ or $y$ can be negative as well)?
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### News on SG values of Grundy's Game?

Is there any recent research into the Sprague-Grundy values of Grundy's game? It was calculated to $2^{35}$ integers but with no sight of recurrence. Has anyone come up with anything new to compute ...
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### Covering the square with “crosses”.

The problem concerns covering the unit square with translates of a specific figure, which I will refer to as a "cross", using as few translates as possible. The difficulty seems to result from the ...
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