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MathGod's user avatar
MathGod's user avatar
MathGod
  • Member for 10 years, 6 months
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74 votes
Accepted

Product of cosines: $ \prod_{r=1}^{7} \cos \left(\frac{r\pi}{15}\right) $

63 votes
Accepted

Find all the integral solutions to $x^6-y^6+3x^4y-3y^4x+y^3+3x^2+3x+1=0$

28 votes

A conjectured closed form of $\int\limits_0^\infty\frac{x-1}{\sqrt{2^x-1}\ \ln\left(2^x-1\right)}dx$

24 votes
Accepted

Evaluate $\lim_{x\to 0}\frac {(\cos(x))^{\sin(x)} - \sqrt{1 - x^3}}{x^6}$

20 votes
Accepted

Solve $x^7-5x^4-x^3+4x+1=0$ for $x$

18 votes
Accepted

A limit without invoking L'Hopital: $\lim_{x \to 0} \frac{x \cos x - \sin x}{x^2}$

18 votes
Accepted

What is $\sum_{r=0}^n \frac{(-1)^r}{\binom{n}{r}}$?

15 votes

Solving following quartic equation

13 votes

Generalized Euler sum $\sum_{n=1}^\infty \frac{H_n}{n^q}$

13 votes

Ordinary generating function for $\binom{3n}{n}$

13 votes
Accepted

Evaluating $ \sum\limits_{n=1}^\infty \frac{1}{n^2 2^n} $

13 votes
Accepted

Solve $ 1 + \frac{\sqrt{x+3}}{1+\sqrt{1-x}} = x + \frac{\sqrt{2x+2}}{1+\sqrt{2-2x}} $

10 votes

Math Olympiad Algebraic Question Comprising Square Roots

10 votes

Show that $\sqrt{4+2\sqrt{3}}-\sqrt{3}$ is rational using the rational zeros theorem

8 votes
Accepted

Evaluate $\lim_{n \to \infty} \int_{0}^1 \frac{n+1}{2^{n+1}} \left(\frac{(t+1)^{n+1}-(1-t)^{n+1}}{t}\right) \mathrm{d}t$

8 votes
Accepted

What is the minimum value of $abc$

7 votes
Accepted

Show $(1+x_1)(1+x_2)...(1+x_n)\geq2^n$ given $x_1x_2...x_n=1$

7 votes

Question about (probably false) elementary proof of Fermat's Last Theorem

6 votes

Prove that $(mn)!$ is divisible by $(n!)\cdot(m!)^n$

6 votes
Accepted

Evaluate $\int_{0}^{\frac{\pi}{2}} \frac{\sin^2 nx}{\sin^2 x}\text{d}x$

5 votes
Accepted

Calculate the sum : $S=1+\frac{\sin x}{\sin x}+\frac{\sin2x}{\sin^2 x}+\cdots +\frac{\sin nx}{\sin^n x}$

5 votes
Accepted

Solve $2^x+7=y^2$ for integer $(x,y)$

5 votes
Accepted

A proof involving the Euler phi function

5 votes

Finding roots of cubic equation

5 votes
Accepted

Prove $\forall x,c \in \mathbb R, |f(x) - f(c)| \le K|x - c|^2$ implies $f(x)$ is constant.

5 votes

Combinatorics problems that can be solved via infinite descent

5 votes

Prove result of xy

4 votes
Accepted

polynomial of fifth degree

4 votes
Accepted

Finding the value of $y=b^2(3a^2+4ab+2b^2)$ if $a^2(2a^2+4ab+3b^2)=3$ and $a$ and $b$ are distinct zeros of $x^3-2x+c$

4 votes
Accepted

How to prove $\sum_{k=1}^{n}k\binom{n}{k} = n2^{n-1}$