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QC_QAOA
  • Member for 7 years, 7 months
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  • Within 8.2kparsecs of Sgr A
13 votes
Accepted

Find $f(x)$ such that it maximizes $\int_0^1 \left(f(f(x))-f(x)\right) dx$

11 votes
Accepted

Investigating the recurrence relation $x_{n+1}=\frac{x_{n}+x_{n-1}}{(x_{n},\,x_{n-1})}+1$

11 votes

Is $a$ bigger than $0$ or not?

9 votes

Find $\lim_{x\rightarrow 0}x^{x^{x^x}}$

9 votes
Accepted

If $a^2-a-1=0$ where $a\gt0$, then what does $a^6$ equal? (Olympiad question)

8 votes

Why is $0^i$ undefined?

8 votes
Accepted

Convergence of $\sum\frac{1}{n(\ln n)^c}$

8 votes

True or False?: There are infinitely many continuous functions $f$ for which $\int_0^1f(x)(1-f(x))dx=\frac{1}{4}$

7 votes
Accepted

Sum of the series $\sum_{n=0}^{\infty} \lfloor nr \rfloor x^n$ where $r$ is rational?

7 votes

Show that $\sum_{n=1}^{\infty} \frac{(-1)^{n}}{\sqrt{n}}\sin(1 + \frac{x}{n})$ converges uniformly on $\mathbb{R}$

7 votes

How to assign 3 rooms to 3 people with 1 coin randomly?

7 votes
Accepted

If $\frac{x^2+y^2+x+y-1}{xy-1}$ is an integer for positive integers $x$ and $y$, then its value is $7$.

6 votes
Accepted

Polynomial that indicates whether or not $x = 1 \pmod n$.

6 votes
Accepted

$\underset{n=1}{\overset{\infty}{\sum}}\frac{a_n}{n!}\in\mathbb{Q}\Longleftrightarrow\exists N\in\mathbb{N}\backepsilon a_n=n-1\forall n\ge N$

6 votes
Accepted

If $\sum\limits_{n=1}^{\infty}\frac{1}{p(n)}\in\mathbb{Q}$, is $\sum\limits_{n=1}^{\infty}\frac{n}{p(n)}\in\mathbb{Q}$?

6 votes

Find $n$ and $m$, if $n,m$ are natural numbers, such that $m^6 + 279 = 2^n$.

6 votes

Proving $\def\n#1{\left(\frac12+\sum\limits_{k=1}^n{#1}^{k^2}\right)}\n{a}\n{b}\ge{\n{(ab)}}^2$

6 votes

How can we show that there is a zero of $f$

6 votes
Accepted

If $f(x)>0$ is increasing and $g(x)>0$ is decreasing, then, is it clear if $f(x)g(x)$ is increasing or decreasing?

6 votes
Accepted

Does $\ \sum_{n=1}^{\infty} \frac{\sin(2^n x)}{n}\ $ converge for all $x\ ?$

6 votes
Accepted

Is this real numbers proof formal enough?

6 votes

Prove that $a_{n+1} = a_n^2 - a_n+1$ for all $n$ large enough

6 votes

Why is the set of real numbers non-enumerable?

6 votes

Why do calculus textbooks gloss over absolute values?

6 votes
Accepted

True or false: For every $n\in\mathbb{Z^+}$, there exist $a,b,c$ such that $y=(x-a)^2+b$ and $y=c$ enclose exactly $n$ lattice points.

5 votes
Accepted

If $a_n\to a$ then $b_n=\frac{1}{n^2}\sum_{i=1}^n ia_i \to a/2$.

5 votes
Accepted

What's the percentage of primes in ranges $[0,\frac{n}{2}]$ and $[\frac{n}{2},n]$?

5 votes
Accepted

Prove that $|\sin 1| + |\sin 2| + |\sin 3| +\cdots+ |\sin 3n| > 8n/5$

5 votes

Is $2^n$ always a sum of exactly $n$ primes for $n \geq 2$?

5 votes
Accepted

Two rectangles: The $1$st has twice the perimeter of the $2$nd and the $2$nd has twice the area of the $1$st.

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