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Somos
  • Member for 6 years, 10 months
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48 votes

Is there any conjecture that has been proved to be solvable/provable but whose direct solution/proof is not yet known?

23 votes

If $f(x)-f^{-1}(x)=e^{x}-1$, what is $f(x)$?

21 votes
Accepted

How to construct a transcendental number

19 votes

Is OEIS A248049 an integer sequence?

17 votes

Show that the three medians of a triangle are concurrent at a point

15 votes
Accepted

Does the order of the Fibonacci sequence's initial values matter?

12 votes

Let $a_1=\sqrt{6},a_{n+1}=\sqrt{6+a_n}$. Find $\lim\limits_{n \to \infty} (a_n-3)6^n$.

12 votes

Is there a formal term for the placement of two symbols next to each other to imply an operation?

11 votes

Should a mathematical proof be 'convincing'?

11 votes
Accepted

Does the Rogers-Ramanujan continued fraction $R(q)$ satisfy this conjectured infinite series

11 votes

How did Ramanujan find this formula?

11 votes

How does one transform a sum into a telescoping sum?

10 votes
Accepted

Find $f(x)$ satisfying $f(f(x))=x^x$

9 votes

Ratio of theta functions as roots of polynomials

8 votes

Is group associativity equivalent to assuming equivalence of left and right inverses?

8 votes
Accepted

Where does the Weierstrass expansion of $\operatorname{sn}$ come from?

8 votes
Accepted

Evaluate $\lim_{n \to \infty} \frac{a_n}{2 ^ {n - 1}}$ if $a_n = a_{n - 1} + \sqrt{a_{n - 1}^2 + 1}$

8 votes

What are some other ways to compute the factorials using addition only?

8 votes

Ways to arrive at the existence of irrational numbers

8 votes

What is a good way to introduce Euler's totient function?

8 votes
Accepted

Is there a group $G$ and subgroup $H$, such that there exists $g\in G$ with $gHg^{-1} \subset H$ and $|H:gHg^{-1}|$ is infinite?

8 votes

Three externally touching circles have their centers on the same line and have radii $a$,$b$ and $c$ (where $a<b<c$).Prove that $b^2=ac$.

7 votes
Accepted

Difference between generating functions and formal power series

7 votes

show this sequence always is rational number

7 votes
Accepted

An interesting recurrent equality, possibly easier to solve in its differential form?

7 votes
Accepted

Find estimates for the solution $x=x_n$ of the equation $(1+x)^n =1+(n+1)x$

7 votes

Is there a continuous way to represent a triangle with a vector with no ambiguity?

7 votes

Why is the euler characteristic of a sphere 2?

7 votes

What are some interesting and unusual theorems, identities, notations in Trigonometry?

7 votes
Accepted

How to derive this series

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