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ZFR
  • Member for 8 years, 4 months
  • Last seen this week
  • New York, NY, USA
15 votes
Accepted

$A+B+C+7$ is perfect square where $A,B,C$ numbers with repeating digits.

10 votes

If $\lim_{x \to \infty} (f(x)-g(x)) = 0$ then $\lim_{x \to \infty} (f^2(x)-g^2(x)) = 0\ $: False?

10 votes

Looking for a non-combinatorial proof that $a! \cdot b! \mid (a+b)!$

6 votes

Does $|f'(x)|<1$ imply $f$ has a fixed point?

6 votes
Accepted

If $\varphi(mn)=\lambda \varphi(m)\varphi(n)$ what should be written for $\lambda$

5 votes
Accepted

Identity with integer part

5 votes
Accepted

How to prove or disprove $\forall x\in\Bbb{R}, \forall n\in\Bbb{N},n\gt 0\implies \lfloor\frac{\lfloor x\rfloor}{n}\rfloor=\lfloor\frac{x}{n}\rfloor$.

5 votes
Accepted

If $A^2$ is orthogonal is it true that $A$ is also orthogonal?

4 votes
Accepted

Brief moment from theorem 8.5 on PMA Rudin

4 votes

convergence test for $\sum\frac{\sin(5^n)}{n!}$?

4 votes
Accepted

Solve in integers the equation $2x+3y = 5$

3 votes

Show $f(x)=\sqrt{x}$ is continuous on $[0,1]$

3 votes
Accepted

Equality in Young's inequality

3 votes

Prove that product of $L_1$ norms is greater than $1$

3 votes
Accepted

Solutions of some diophantine equation

3 votes
Accepted

Interesting property of finite integer sequence with sum 1

3 votes

Identity of Fibonacci sequence

3 votes
Accepted

Find closed form of $f(a,b,c)$

3 votes
Accepted

Find the least value of $\frac{1}{x}+\frac{3}{y}+\frac{5}{z}$

3 votes
Accepted

Let $H\le G, g\in G$ with order $n$, and $gH\in G / H$ with order $d$. Show $d$ divides $n$.

2 votes
Accepted

Find the range of the $\alpha$ which makes the $\sum_{n=1}^\infty (1-\cos(\frac{1}{n}))(\sin(\frac{1}{n^\alpha}))$ converge.

2 votes

Product of Sum of Digits

2 votes

Limit of trigonometrical function $\sin(\pi x)/{(1-x)}$ as $x\to1$?

2 votes
Accepted

Prove that $(xy+yz+xz)(x^2+y^2+z^2+x+y+z)≥2(x+y+z)^2$

2 votes

Limit of $\underset{n\to \infty }{\text{lim}}\frac{\ln (n+1)}{\ln (n)}$ without L'Hôpital

2 votes
Accepted

$a_1<a_2<a_3<a_4$ such that $\sum_{i=1}^4\frac{1}{a_i}=\frac{11}{6}$

2 votes

Union of sets having $\binom{n - 1}{2}$ elements with each two of them having $n - 2$ common elements has cardinality of at least $\binom{n}{3}$.

2 votes
Accepted

Prove that a power of $2$ cannot end in four equal digits

2 votes

Binary quadratic form of $p$

2 votes
Accepted

Proving that $f: E\to \mathbb R$, defined by $f(x)=\frac{1}{x-x_0}$ is not uniformly continuous on $E$.