Oleg567's user avatar
Oleg567's user avatar
Oleg567's user avatar
Oleg567
  • Member for 11 years, 4 months
  • Last seen more than a week ago
85 votes
Accepted

How to find out which number is larger without a calculator?

57 votes
Accepted

Show that the product of two consecutive natural numbers is never a square.

43 votes

One question to know if the number is 1, 2 or 3

40 votes

Visual explanation of the following statement:

40 votes
Accepted

Can all circles of radius $1/n$ be packed in a unit disk, excluding the circle of radius $1/1$?

37 votes
Accepted

If $x \neq 0,y \neq 0,$ then $x^2+xy+y^2$ is .....

27 votes

Fibonacci number that ends with 2014 zeros?

27 votes

Is the sum of two sine waves periodic?

25 votes

Pi Estimation using Integers

23 votes

How to solve this sequence $165,195,255,285,345,x$

20 votes
Accepted

$3 \times 3$ matrix with determinant a large power of $2$

19 votes
Accepted

What is the simplest ellipse that goes through exactly 13 lattice points?

18 votes

Prime as sum of three numbers whose product is a cube

17 votes

Find integer in the form: $\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b}$

16 votes
Accepted

What's the closest approximation to $\pi$ using the digits $0-9$ only once?

16 votes

Can all circles of radius $1/n$ be packed in a unit disk, excluding the circle of radius $1/1$?

15 votes
Accepted

How to prove $\frac{1+\sin{6^\circ}+\cos{12^\circ}}{\cos{6^\circ}+\sin{12^\circ}}=\sqrt{3}$?

12 votes
Accepted

Proving that $\sum_{k=1}^{\infty} \frac{3408 k^2+1974 k-720}{128 k^6+480 k^5+680 k^4+450 k^3+137 k^2+15 k} = \pi$

11 votes
Accepted

Area of an irregular polygon

11 votes

Proving gcd($a,b$)lcm($a,b$) = $|ab|$

11 votes

Formula for the sequence 1 1 2 2 3 3

10 votes
Accepted

Solving an equation in $x$, in which $x$ occurs as exponent four times

9 votes
Accepted

How to prove that $3ab(a+b)$ cannot be a cube?

9 votes

The identity $\tan({\pi\over4}-{a\over2}) = \sec(a)-\tan(a)$

9 votes

$1$ as difference of composites with same number of prime factors and smallest examples

9 votes
Accepted

Is there a simple pattern to memorize the sine of $0^\circ$, $15^\circ$, $30^\circ$, $45^\circ$, $60^\circ$, $75^\circ$, $90^\circ$?

9 votes
Accepted

On $1^2+2^2+\dots+24^2 = 70^2$, and $15^3+16^3+\dots+34^3 = 70^3$

9 votes

Rolling ellipses

8 votes
Accepted

Prove $\sum_{i=1}^{n}\frac{a_{i}}{a_{i+1}}\ge\sum_{i=1}^{n}\frac{1-a_{i+1}}{1-a_{i}}$ if $a_{i}>0$ and $a_{1}+a_{2}+\cdots+a_{n}=1$

8 votes

Inequality $\frac{a}{b} + \frac{b}{c} + \frac{c}{a} \geq a + b+ c$ when $abc = 1$

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