Jaakko Seppälä
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 Mar 11 comment How do I prove that any chessboard of size $n \times 3$, where n is even and $n \geq 10$, has a closed knight's tour? @LaurentDuval Thanks. I edited the answer. Mar 11 revised How do I prove that any chessboard of size $n \times 3$, where n is even and $n \geq 10$, has a closed knight's tour? added 92 characters in body Mar 11 comment How do I prove that any chessboard of size $n \times 3$, where n is even and $n \geq 10$, has a closed knight's tour? @JyrkiLahtonen I tried to search it but unfortunately I was unable to find it anymore. Mar 11 revised How do I prove that any chessboard of size $n \times 3$, where n is even and $n \geq 10$, has a closed knight's tour? added 14 characters in body Mar 7 comment Prove that $(\mathbb{Z},+)$ and $(\mathbb{Q},+)$ are not isomorphic. math.stackexchange.com/questions/620551/… Aug 17 comment Prove area of a quadrilateral is $\frac14[4m^2n^2-(b^2+d^2-a^2-c^2)^2]^{\frac12}$ There seems to be a proof in artofproblemsolving.com/wiki/index.php/… 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 $1582\cdot 17^2\equiv 0\pmod 2$. 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 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