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dan_fulea
  • Member for 6 years, 1 month
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20 votes
Accepted

A conjecture related to a circle intrinsically bound to any triangle

16 votes
Accepted

For $A \in \mathcal{M}_3(\mathbb{C})$, does $\mathrm{tr}(A^2) = \mathrm{tr}(A^3) \in \mathbb{Q}$ imply $\mathrm{tr}(A^4) \in \mathbb{Q}$?

14 votes
Accepted

Help with Seemingly Hopeless Double Integral

13 votes
Accepted

Let $a$ be a $p$-cycle in $S_p$, and let $b$ be a transposition in $S_p$. Show $S_p$ is generated by $a$ and $b$.

12 votes

Show that the polynomial $P(x):=x^4-6x+6$ has no real roots .

12 votes
Accepted

Do permutations on the decimal expansions of irrational numbers retain the property of irrationality?

11 votes
Accepted

A ring such that $(a+b)^2=a^2+b^2$ and $(a+b)^3=a^3+b^3$

11 votes
Accepted

Challenging problem: Calculate $\int_0^{2\pi}x^2 \cos(x)\operatorname{Li}_2(\cos(x))dx$

10 votes

Evaluate $\sum\limits_{n=1}^{\infty}\frac{1}{n^3}\binom{2n}{n}^{-1}$.

9 votes
Accepted

Class Group of the Class Number $3$ with their elements given explicitly

9 votes

alternate deletion of integers between 1 and 128, which is the last one?

9 votes
Accepted

Prove a trigonometric identity: $\cos^2A+\cos^2B+\cos^2C+2\cos A\cos B\cos C=1$ when $A+B+C=\pi$

8 votes
Accepted

Sum of the inverse squares of the hypotenuse of Pythagorean triangles

8 votes
Accepted

If there exists a positive integer $n$ such that any element $x$ of a ring $R$ satisfies $x^{4^n+2} = x$, then every element $x$ in $R$ is idempotent

8 votes
Accepted

How many numbers can we select from $\{1,2,...2016\}$ such that sum of any four of them cannot be divided by $11$

8 votes

How to find $\operatorname{P.V.}\int_0^1 \frac{1}{x (1-x)}\arctan \left(\frac{8 x^2-4 x^3+14 x-8}{2 x^4-3 x^3-11 x^2+16 x+16}\right) \textrm{d}x$?

8 votes
Accepted

An olympiad number theory problem asking for prime numbers with a certain property

8 votes
Accepted

Are there any perfect cubes form of $611\dots1$?

8 votes
Accepted

number of rational points of hyper elliptic curve $y^5=-x^2+x$ over $\Bbb{F}_{121}$

7 votes
Accepted

Solving the summation $ S = \sum_{r=1}^{25} \frac{1}{z^{18r} + z^{9r} + 1} $

7 votes

Why is $\langle a,b,c,d\mid abcda^{-1}b^{-1}c^{-1}d^{-1}\rangle\cong \langle a,b,c,d\mid aba^{-1}b^{-1}cdc^{-1}d^{-1}\rangle$?

7 votes

We call a coloring of $3$-regular graph with $3$ colors good if for every $3$ edges incident with a vertex ...

7 votes
Accepted

Why $p\equiv 3$ mod $8$ is not a congruent number

7 votes

Challenging problem: Calculate $\int_0^{2\pi}x^2 \cos(x)\operatorname{Li}_2(\cos(x))dx$

7 votes

Finding the Center of Mass of a disk when a part of it is cut out.

7 votes

Prove: $\int_0^2 \frac{dx}{\sqrt{1+x^3}}=\frac{\Gamma\left(\frac{1}{6}\right)\Gamma\left(\frac{1}{3}\right)}{6\Gamma\left(\frac{1}{2}\right)}$

7 votes
Accepted

Prove that $\angle ABC <$ $ 84^\circ$.

7 votes
Accepted

Proving that $8^x+4^x\geq 5^x+6^x$ for $x\geq 0$.

7 votes

Geometric way to view the truncated braid groups?

7 votes
Accepted

If 2C8$\cdot$3C1$=$90C58, what is C?

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