Newest Questions
1,697,173 questions
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Cancelling factors in isogenies between elliptic curves
I am currently working with isogenies of supersingular elliptic curves over finite fields and I do not really understand when and how I am allowed to cancel single factors.
For exapmle, let $\phi,\psi:...
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Understanding modular curves as "moduli of Hodge structures"
It is well-known that modular curves parametrize elliptic curves with level structures. For the purpose of this question, I will work complex-analytically and describe analytically the moduli space $$\...
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a recurrence relation how to solve it [closed]
How can I solve this recurrence:
$$na_n=a_{n-1}+a_{n-2}$$
with $a_0=a$ and $a_1=b$ ?
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Countablity of w*
Consider the set w* of finite sequence of whole numbers is this uncountable
If it was N* then countable we can enumerate sum wise like
1 with (1)
2 with (2),(1,1)
3 with sum 3 sequence etc
but how we ...
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A question on intuition behind the Fundamental Theorem of Calculus
I’ve been struggling with the intuition behind the Fundamental Theorem of Calculus for almost nine years now. It has kept bothering me ever since I first encountered it, and I’m still looking for an ...
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$\Re (\zeta (s)) > 0$ for $\sigma > 1$
Inspired from this question and this question, I notice that $\Re (\zeta (s)) > 0$ for $\sigma > 1$. Here's the best proof I could find:
For $\sigma > 1$:
$$\ln (\zeta (s)) = \sum_{p} \sum_{n ...
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The existence of a law of composition such that every permutation is an isomorphism implies that the base set has 0, 1 or 3 elements
This is the exercise 4 in Chapter 1, section 2, Algebra by Bourbaki. Here is the original statement:
The exercise:
For there to exist on a set $E$ a law of composition such that every permutation of $...
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Ascending chain for finitely generated modules.
Recently I'm reviewing some concepts in module theory, and I found a post Maximal submodule in a finitely generated module over a ring, where an answerer @rschwieb states that:
A module $M$ is ...
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Iranian combinatorics olympiad 2024 problem 3
We say that a sequence $x_1, x_2,\ldots, x_n$ is increasing if $x_i ≤ x_{i+1}$ for all $1 ≤ i < n$. How many ways are there to fill an 8 x 8 table with numbers 1, 2, 3, and 4 such that:
• The ...
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What is the exact measure of angle Ô in the second case?
In each of these two configurations which seem to be similar, we ask for the measure of angle Ô in the triangle AOB .
( The points O , D , A are collinear in this order as well as O , E , B ).
So , by ...
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Nested radicals built from primes and a possible convergence pattern
Let us look at nested radicals of the form
$$x=\sqrt{n_1+\sqrt{n_2+\sqrt{n_3+\dots}}}$$
where each $n_i$ is a positive integer. Classically (Herschfeld, Amer. Math. Monthly 42 (1935)), such sequences ...
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How many colours do we need to colour the points in $\mathbb{Z}^{n}$?
This question comes from two problems I've met.
The first problem is: $n$ is a given positive integer, $A$ is a set of $n$ integers, find the minimal $m$, such that for any $A$, it's possible to ...
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Is the MRB constant possibly rational, given its Abel-regularized double-series form?
The MRB constant is defined by
$ S = \sum_{n=1}^{\infty} (-1)^n (n^{1/n} - 1) \approx 0.187859642\dots $
It converges conditionally, but it can also be expressed via an Abel-regularized double series ...
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How do I prove the change of variables into polar coordinates using measure theory?
From this answer I have that $ \int_Yf(y)\mathrm{d}(g\mu)(y)=\int_Xf(g(x))\mathrm{d}\mu(x)$, where $g$ is a map between measurable spaces and $g\mu$ is the image measure.
With $X=[0,r]\times[0,2\theta]...
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How could this group scheme over $R_h$ decent to $R$? (Group Schemes, Formal Groups, and p-Divisible Groups written by S. S. Shatz)
As the title has mentioned, this is a problem I encountered in the section 3 of "Group Schemes, Formal Groups, and p-Divisible Groups" written by S. S. Shatz.
Since the background of this ...
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