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alien2003
  • Member for 3 years, 4 months
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14 votes
5 answers
383 views

Prove that $\frac{a}{\sqrt{a^2+b^2}}+\frac{b}{\sqrt{b^2+c^2}}+\frac{c}{\sqrt{c^2+d^2}}+\frac{d}{\sqrt{d^2+a^2}}\leq3$

5 votes
2 answers
86 views

We have $2$ $K_n$ graphs sharing exactly one vertex. Prove that no matter how we label the vertices, there are $2$ edges with the same mark

5 votes
2 answers
169 views

Let G be a non abelian group with a square-free order. Prove that there are two elements $a,b\in G$ such that $ab\neq ba$ and $ord(a)=ord(b)$.

5 votes
1 answer
203 views

Geometrical combinatorics with $(n+1)^2$ points inside a square that determine a triangle [duplicate]

5 votes
1 answer
118 views

Prove that there is an infinite number of values of $n$ for which the biggest prime divisor $p$ of $2^{n}-1$ satisfies $p < 2^{n/2021}-1$

5 votes
0 answers
88 views

Prove that a semigroup $S$ in which $x^3=x$ and $x^2y^2=y^2x^2$ for every $x,y \in S$ is commutative. [duplicate]

3 votes
1 answer
102 views

Find all differentiable functions $g: \mathbb{R} \rightarrow \mathbb{R}$, for which $g'$ is continuous such that $g'(x)\geq (g(x))^2$ for every $x$

3 votes
1 answer
160 views

Property of bicentric quadrilateral involving the Miquel point of $OMXN$

3 votes
2 answers
198 views

Infinite set such that sum of elements of every finite subset is not a power of $p$

2 votes
1 answer
106 views

Circumscribed circles of the triangles [closed]

2 votes
1 answer
74 views

Minimal chain covering of all subsets of {$1,2,3,4,....,2n,2n+1$}

2 votes
1 answer
97 views

A game with numbers modulo $N$

2 votes
1 answer
88 views

Prove that there are infinitely many $n\in\mathbb{N^*}$ such that $n|2^{2n-1}+1$

2 votes
1 answer
53 views

Equation with polynomial with integer coeficients.

1 vote
2 answers
147 views

Find the determinant of a sum of idempotent matrices

1 vote
2 answers
317 views

Number of triangles in $K_n$ that don't share any edges

1 vote
1 answer
179 views

Number theory with sequences

1 vote
1 answer
113 views

Prove that $A$ is on the radical axis of two circles

1 vote
3 answers
256 views

Prove that $\Delta ABC$ is an equilateral triangle if and only if the complex coordinates $a$,$b$, and $c$ satisfy a relation.

1 vote
0 answers
41 views

Minimal polynomial of a complex number $z$ that is also an algebraic integer does not have $z$ as a repeated root [duplicate]

0 votes
1 answer
113 views

Solve the equation in real numbers: $x-6+\frac{2}{\sqrt{x-2}}=\frac{1}{3}\log_3(\frac{x}{x^3+54})$

0 votes
1 answer
181 views

Determinant of matrix similar to Vandermonde determinant [duplicate]