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richrow's user avatar
richrow
  • Member for 5 years, 6 months
  • Last seen this week
8 votes
Accepted

How to find this $\prod_{k=-\infty}^{+\infty}\frac{x^2+(4k+1-y)^2}{x^2+(4k+3-y)^2}$

7 votes

Prove that every tournament contains at least one Hamiltonian path.

7 votes

Zolotarev's Lemma and Quadratic Reciprocity

6 votes
Accepted

Show that the elements of the sequence are divisible by $2^n$

6 votes
Accepted

Is $\sum_{\substack{n_1+\ldots+n_k=2m\\ n_1,\ldots,n_k\in\mathbb Z_{\geq 0}}}x_1^{n_1}\cdots x_k^{n_k} \geq 0$ for all $x\in\mathbb R^k$?

5 votes

Can the number of terms of sequence $p_1$, $2p_1+1$, $2(2p_1+1)+1$, . . . be more than 3?

5 votes
Accepted

Prove that the midpoint of $AH$ lies on the radical axis of $(REC)$ and $(QFB)$.

5 votes

Show that $(\binom{p^2}{p} -p ) $ is divisible by $p^5$, for every prime number $p, p\ge 5$

4 votes

Proving inequality $(a+\frac{1}{a})^2 + (b+\frac{1}{b})^2 \geq \frac{25}{2}$ for $a+b=1$

4 votes
Accepted

Prove that the value of the expression $|a_1-b_1|+|a_2-b_2|+\dots+|a_n-b_n|$ does not depend on the coloring.

4 votes
Accepted

$f(x,y) - f(x,z) = g(y,z)$ implies $f(x,y) = a(x) + b(y)$

4 votes
Accepted

can incentre lie on the Euler line for an obtuse triangle?

4 votes
Accepted

Prove that $n$ is a power of 2 in the following sets of sums

4 votes

A geometry problem with the reflection of the incenter

4 votes

Can anyone explain why expressions of the form $\sqrt[3]{x-\sqrt{y}}+\sqrt[3]{x+\sqrt{y}}$ can be rational?

4 votes
Accepted

Positive integer solutions to $y^2=a(1+xy-x^2)$

4 votes
Accepted

Show that $\frac{46!}{48}+1$ is not a power of 47

4 votes

Let $a$ and $b$ be positive integers such that $an + 1$ s a cube if and only if $ bn + 1$ is a cube. Prove that $a = b.$

4 votes

Prove that $\sum \frac{a^3}{a^2+b^2}\le \frac12 \sum \frac{b^2}{a}$

4 votes
Accepted

Find minimum of $\sqrt{a}+\sqrt{b}+\sqrt{c}$, given that $a,b,c \ge 0$ and $ab+bc+ca+abc=4$

4 votes

L^2 function also bounded almost everywhere?

3 votes
Accepted

Find all triples $(a, b, c)$ of real numbers such that $a + 4b + 18c =\frac{a^2+b^2+c^2}{6}=2022$

3 votes
Accepted

$a,b,c\in \mathbb R^+$ Prove that $\sum_{cyc}\sqrt{a^2+2022}/\sum_{cyc}\sqrt{ab}\ge 2$

3 votes
Accepted

Show that $(b_1+b_2)^2\leq (a_1+a_2)(c_1+c_2)$

3 votes

Evaluate $\lim_{n \to \infty}\prod_{k=0}^{n} \left(1+\frac{2}{45^{2^k}+45^{-2^k}}\right)$

3 votes
Accepted

$(1+x)^d \leq 1 + x^d$ for $x \geq 0$ and $d \in (0,1]$

3 votes

Number of real roots $x^8-x^5+x^2-x+1=0$

3 votes

Proving $\frac{a^3+b^3+c^3}{3}-abc\ge \frac{3}{4}\sqrt{(a-b)^2(b-c)^2(c-a)^2}$

3 votes

Prove that $(A,N;P,B)=(A,M;Q,C)=-1$ .

3 votes

How can I calculate this Riemann sum?

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