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Jul
24
comment if $(1-a)(1-b)(1-c)(1-d) = \frac{9}{16}$ then minimum integer value of $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d} = ?$
@VinodKumarPunia No, as $16+8\sqrt 3\not\in\mathbb Z$. The problem asks to find positive reals $a,b,c,d$ and the smallest integer $n$ satisfying $a,b,c,d>0$, $(1-a)(1-b)(1-c)(1-d)=\frac{9}{16}$, $1/a+1/b+1/c+1/d=n$ assuming the original author wrote the problem correctly.
Jul
7
comment How to prove that $7^{31} > 8^{29}$
$93\cdot 17^3\equiv 1 \pmod 2$ but $1582\cdot 17^2\equiv 0\pmod 2$.
Feb
8
revised Is there always a unit in topological rings?
added 2 characters in body; edited title
Feb
8
asked Is there always a unit in topological rings?
Jan
8
awarded  Popular Question
Oct
14
comment How to easily prove Euler's theorem, $OI^2=R(R-2r)$?
This is a famous result due to Leonhard Euler. It is a matter of taste which proof is the nicest one. You can use for example trigonometry, inversion, or Poncelet's porism. See dpmms.cam.ac.uk/~njb65/Euler.pdf for details.
Oct
14
comment How to easily prove Euler's theorem, $OI^2=R(R-2r)$?
And BTW, the formula is $OI^2=R(R-2r)$ so remember that square term.
Oct
14
comment How to easily prove Euler's theorem, $OI^2=R(R-2r)$?
There are different proofs in dpmms.cam.ac.uk/~njb65/Euler.pdf
Jul
10
comment IMO 2014 problem 3, first day
Have you seen artofproblemsolving.com/Forum/viewtopic.php?f=1098&t=596927 ?
Jul
2
awarded  Curious
Jun
21
awarded  Tumbleweed
Jan
8
comment Prove that $ \displaystyle \lim\limits_{n \rightarrow \infty} \left(\frac{23n+2}{4n+1}\right) = \frac{23}{4} $.
It is not correct. You have to define symbols before you use them. Therefore, there is a mistake on the line $$ \displaystyle \vert \frac{23n+2}{4n+1} - \frac{23}{4} \vert < \epsilon.$$ Before that you have to write for example "Choose an arbitrary positive real number $\epsilon$".
Oct
27
comment Question about Right Angles
I think you have to define the right angle without degrees and you have to define how to measure angles. Otherwise I can say your current definition is wrong as the measure of right angle is $\pi/2.$
Oct
8
comment Combinatorial proof of $\sum\limits_{k=0}^n \binom{2k}{k} \binom{2n-2k}{n-k} =4^n$
math.stackexchange.com/questions/72367/…
Oct
2
awarded  Nice Answer
Oct
2
awarded  Yearling
Oct
2
revised Inequality…(RMO $1994$…question $8$)
added 101 characters in body
Oct
2
revised Inequality…(RMO $1994$…question $8$)
added 2 characters in body
Oct
2
answered Inequality…(RMO $1994$…question $8$)
Sep
13
awarded  Critic