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CY Aries
  • Member for 6 years, 10 months
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81 votes
Accepted

Witty functional equation

53 votes

Show that $(2,0,4) , (4,1,-1) , (6,7,7)$ form a right triangle

16 votes

What is the area of the shaded region in this rectangle?

16 votes
Accepted

Does any (right) triangle exist such that $a^3+b^3=c^3$?

15 votes
Accepted

Proof that $\log_a b \cdot \log_b a = 1$

15 votes
Accepted

Hint for integration $\int_{-2}^{2} \frac{3x^2}{1+e^x}\mathrm dx$

14 votes
Accepted

Exercise 5.3 in Calculus Made Easy: are these answers equivalent?

12 votes
Accepted

Why is a set not a partition of itself?

12 votes

How to solve this absolute value equation

11 votes

Classical examples of mathematical induction

11 votes
Accepted

What implications has an irrational slope?

10 votes
Accepted

Integral part of sum of huge powers

10 votes
Accepted

If a triangle is not equilateral, must its orthocenter and circumcenter be distinct?

10 votes

How to find value of floor function of a given number?

10 votes
Accepted

A field has no "zero divisors"

10 votes

Evaluation of the limit by using epsilon-M approach.

10 votes
Accepted

Minimize $m+n$ given $\frac{2016}{2017}<\frac mn<\frac{2017}{2018}$

9 votes

Algebra: Prove inequality $\sum_{n=1}^{2015} \frac1{n^3} < \frac 54$

9 votes
Accepted

limit $\lim_{n\to\infty}\frac{1}{\sqrt n}\left(\frac{1}{\sqrt 2+\sqrt4}+\frac{1}{\sqrt4+\sqrt6}+\cdots+\frac{1}{\sqrt{2n}+\sqrt{2n+2}}\right)$

9 votes
Accepted

Convergent or Divergent Sequence: $n^3\sin\left(\frac{5}{n^3}\right)$

9 votes
Accepted

Limit of function with Square roots

8 votes

Find the rational number of a, b, c, solving $\sqrt[3]{\sqrt[3]{2}-1}=\sqrt[3]{a}+ \sqrt[3]{b}+\sqrt[3]{c}$

8 votes

>Solve the following equation on the set of real numbers R ${{\left| x-2017 \right|}^{2017}}+{{\left| x-2018 \right|}^{2018}}=1$.

8 votes

Functional equation: $ f(x^2+x+3)+2f(x^2-3x+5)= 6x^2 -10 x + 17$

8 votes
Accepted

Using the fact that $\sqrt{n}$ is an irrational number whenever $n$ is not a perfect square, show $\sqrt{3} + \sqrt{7} + \sqrt{21}$ is irrational.

8 votes

Simplify $\sqrt {9 + 2(1 + \sqrt {3})(1 + \sqrt {7})}$

8 votes

positive root of the equation $x^2+x-3-\sqrt{3}=0$

8 votes
Accepted

Sum of three weighted logarithms with three different bases is equal to an integer

8 votes
Accepted

What are the area of a triangle with side lengths $\tan(x)$, $\cos(x)$ and $\sin(x)$?

7 votes
Accepted

Prove $\sum\limits_{n=1}^\infty \ln({1+\frac 1 {{n}}})$ is divergent.

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