All Questions
Tagged with infinite-sequences nt.number-theory
8 questions
1
vote
1
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167
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Modular arithmetic and elementary symmetric functions
Denote the elementary symmetric functions in $n$ variables by $e_k(x_1, x_2,\dots, x_n)$. In the special case $x_j=j$, simply write $e_k(n)$ for $e_k(1, 2, \dots, n)$. Next, define the sequence
$$a_{+}...
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2
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2
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257
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Reference request for function by which to compute coefficients of continued fraction of algebaic number
The simple continued fraction is in the form
$$[1;1,2,3,4,5,\dots]=1+\cfrac{1}{1+\cfrac{1}{2+\cdots}}, $$ for instance. Obviously,the coefficients $x_i$can be computed by computable function $x_i=f(i),...
- 3,084
1
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0
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162
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Is there any irrational algebraic number among the set? [closed]
Suppose $S$ is set of numbers such that every number in it expands in decimal digits,every digit is 0 or 1,and $\lim_{n\rightarrow\infty}\frac{C_{n}(0)}{n}=\frac{1}{2}$ where ${C_{n}(0)}$ and ${C_{n}(...
- 3,084
4
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0
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132
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Irreducibility of polynomials corresponding to sequences
I have no experience with this, so I dont know if this is too easy for MO.
Let $(a_n)$ be a strictly monotone sequence of natural numbers, then define the set of nice numbers of $(a_n)$ as $X(a_n):=\{...
- 26.5k
2
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2
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984
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Is it necessary that gcd > 1 of an infinite set? [closed]
Consider an infinite set $S$, of positive integers.
If all the finite subsets of $S$ have GCD $>$ $1$, is it necessary that the GCD of $S$ is greater than $1$ as well?
- 23
6
votes
2
answers
2k
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References for the result that $\sqrt{n}$ is equidistributed mod 1
It is not difficult to show (even without Weyl criterion) that the sequence $\sqrt{n}$, $n=1,2,\ldots$ is equidistributed mod 1. However, I need a reference to this result. Can you help me? Thanks.
- 463
15
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984
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Self-avoiding walk on $\mathbb{Z}$
This one is an unanswered question in Math.SE. I've posted it here because I think it deserves more attention.
How many sequences $\{a_n\}$ exist satisfying:
a) $a_1=0$
b) $\forall k\ge1 $ ...
9
votes
1
answer
748
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Magic square on an infinite lattice
This question came to me while reading the discussion of magic square in the complex plane with equal integrals along every horizontal, vertical and diagonal "magic square in the complex plane with ...
- 39.9k