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seen Feb 4 at 23:06

"You have enemies? Good. That means you've stood up for something, sometime in your life" - Winston Churchill


Dec
24
accepted Find all solutions of $1/x+1/y+1/z=1$, where $x$, $y$ and $z$ are positive integers
Mar
28
accepted Show $ I = \int_0^{\pi} \frac{\mathrm{d}x}{1+\cos^2 x} = \frac{\pi}{\sqrt 2}$
Mar
27
accepted What is the largest positive $n$ for which $n^3+100$ is divisible by $n+10$
Mar
27
accepted Prove $1^a+2^a+\cdots+n^a < \frac{(n+1)^{(a+1)}-1}{a+1} $ for any $a >0$ and $n \in \mathbb{Z^+}$
Mar
26
accepted Compute $\sum_{i=1}^{2n} \frac{x^{2i}}{x^i-1}$ where $\{ x \in \mathbb{C}$ | $x^{2n+1} = 1, x \neq 1\}$
Mar
25
accepted What is the probability that a multiple of $864$ is divisible by $1944$
Mar
25
accepted Find the largest divisor of $1001001001$ that does not exceed $10000$.
Mar
24
accepted Show by substitution that $\int_0^{\pi} \frac{x\sin x}{1+\cos^2 x} \,\mathrm dx = \frac{\pi}{2}\int_0^{\pi} \frac{\sin x}{1+\cos^2 x} \,\mathrm dx$
Mar
24
accepted Let $p$ be a prime. Prove that $p$ divides $ab^p−ba^p$ for all integers $a$ and $b$.
Mar
24
accepted Show $\underbrace{{111\cdots}1}_{{\small{p-1} \ 1's}}$ is divisible by $p$
Mar
23
accepted Let $n$ such that $\displaystyle{2^{n-2005}} | n!$
Mar
23
accepted Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
Mar
21
accepted Prove for any positive real numbers $a,b,c$ $\frac{a^3}{a^2+ab+b^2}+\frac{b^3}{b^2+bc+c^2}+\frac{c^3}{c^2+ca+a^2} \geq \frac{a+b+c}{3}$
Mar
18
accepted Evaluating $\int_0^1 \log \log \left(\frac{1}{x}\right) \frac{dx}{1+x^2}$
Mar
18
accepted Let $n$ be a positive integer such that $\displaystyle{\frac{3+4+\cdots+3n}{5+6+\cdots+5n} = \frac{4}{11}}$
Mar
18
accepted Solve the integral $S_k = (-1)^k \int_0^1 (\log(\sin \pi x))^k dx$
Mar
15
accepted Show that $\displaystyle{\frac{1}{9}(10^n+3 \cdot 4^n + 5)}$ is an integer for all $n \geq 1$
Mar
15
accepted Let $a,b,c >0$ Prove the inequality $\displaystyle{\frac{a}{a+1}+\frac{b}{b+1}+\frac{c}{c+1}+\frac{1}{a+b+c+1} \geq 1}$
Mar
14
accepted Wondering if anyone knows how to prove this $y =(\log 2)^{y}$