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### What's your favorite equation, formula, identity or inequality? [closed]

Certain formulas I really enjoy looking at like the Euler-Maclaurin formula or the Leibniz integral rule. What's your favorite equation, formula, identity or inequality?
7k views

### Examples of seemingly elementary problems that are hard to solve?

I'm looking for a list of problems such that a) any undergraduate student who took multivariable calculus and linear algebra can understand the statements, (Edit: the definition of understanding here ...
6k views

### Is there a dense subset of the real plane with all pairwise distances rational?

I heard the following two questions recently from Carl Mummert, who encouraged me to spread them around. Part of his motivation for the questions was to give the subject of computable model theory ...
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### Open problems in Euclidean geometry?

Which are some (research level) open problems in Euclidean geometry ? (Edit: I ask just out of curiosity, to understand how -and if- nowadays this is not a "dead" field yet) I should clarify a ...
9k views

### Convergence of $\sum(n^3\sin^2n)^{-1}$

I saw a while ago in a book by Clifford Pickover, that whether $\displaystyle \sum_{n=1}^\infty\frac1{n^3\sin^2 n}$ converges is open. I would think that the question of its convergence is really ...
3k views

### Status of PL topology

I posted this question on math stackexchange but received no answers. Since I know there are more people knowledgeable in geometric and piecewise-linear (PL) topology here, I'm reposting the question. ...
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Let $s_n = \sum_{i=1}^{n-1} i!$ and let $g_n = \gcd (s_n, n!)$. Then it is easy to see that $g_n$ divides $g_{n+1}$. The first few values of $g_n$, starting at $n=2$ are $1, 3, 3, 3, 9, 9, 9, 9, 9, ... 3answers 4k views ### Can we cover the unit square by these rectangles? The following question was a research exercise (i.e. an open problem) in R. Graham, D.E. Knuth, and O. Patashnik, "Concrete Mathematics", 1988, chapter 1. It is easy to show that$$\sum_{1 \leq k } ... 4answers 1k views ### Freeness of a Z[x]-module Definition: Call a mapping$f: \mathbb{Z} \rightarrow \mathbb{Z}$a generalized polynomial if for any distinct integers$m$and$n$we have$(m - n)|(f(m)-f(n))$. It is easy to check that polynomial ... 2answers 2k views ### Is there a 7-regular graph on 50 vertices with girth 5? What about 57-regular on 3250 vertices? The following problem is homework of a sort -- but homework I can't do! The following problem is in Problem 1.F in Van Lint and Wilson: Let$G$be a graph where every vertex has degree$d$. ... 3answers 696 views ### Largest possible volume of the convex hull of a curve of unit length What is the largest possible volume of the convex hull of an open/closed curve of unit length in$\mathbb{R}^3$? 2answers 1k views ### Induction, the infinitude of the primes, and workaday number theory There are various open problems in the subject of logical number theory concerning the possibility of proving this or that well-known standard results over this or that weak theory of arithmetic, ... 9answers 2k views ### Not especially famous, long-open problems which higher mathematics beginners can understand This is a pair to Not especially famous, long-open problems which anyone can understand So this time I'm asking for open questions so easy to state for students of subjects such as undergraduate ... 2answers 2k views ### Open problems/questions in representation theory and around ? What are open problems in representation theory ? What are the sources (books/papers/sites) discussing this ? Any kinds of problems/questions are welcome - big/small, vague/concrete. Some estimation ... 2answers 481 views ### Emptyness of a projective variety Let$S$be some (fixed) subset of$\mathbb{Z} [X_1, \dots , X_n]$which contains only homogeneous polynomials, and if$F$is a field, let$X(F)$be the set of$ x \in P^{n-1}(F)$such that$f (x) = 0\$ ...

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