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comment Does the function $|x^2-4|/x$ have critical points?
@SanchayanDutta, if you get some graph paper, and just fill in dots for $y = |x^2-4|/x$ when $x=0.2, 0.4,0.6,0.8,1.0, 1.2, 1.4,1.6,1.8,2.0, 2.2,2.4,2.6,2.8,3.0, 3.2,3.4,3.6,3.8, 4.0,4.2 $ you will understand pretty well. printablepaper.net/category/graph
1h
answered Does the function $|x^2-4|/x$ have critical points?
1h
comment Does the function $|x^2-4|/x$ have critical points?
hmmm, first draw $y= |x^2 - 4|$
1h
comment Does the function $|x^2-4|/x$ have critical points?
please DRAW A PICTURE by hand printablepaper.net/category/graph
2h
comment Simultaneously vanishing quadratic forms?
probably not. Also, if the number of $A_i$ is at least the dimension $n,$ then you do not expect any nonzero $c.$ Why do you want to do this?
2h
comment Why is reflection in a plane an automorphism?
@hardmath, alright. Anyway, here is a review of me: zmath.sub.uni-goettingen.de/ZMATH/msc/en/search/zmath/…
2h
comment Why is reflection in a plane an automorphism?
@anon, I also recommend Lattices and Codes by W. Ebeling. I used, with permission, his description of Conway's trick for lattice automorphism groups, in a recent paper with Pete L. Clark. From the second edition, Section 4.5, Automorphism Groups.
2h
comment Why is reflection in a plane an automorphism?
@anon, probably not. A very complete treatment without Lie algebras is Humphreys, Reflection Groups and Coxeter Groups.
3h
revised Why is reflection in a plane an automorphism?
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3h
comment Why is reflection in a plane an automorphism?
given that it is Weyl writing, the reflection preserves the inner product; but more, if it is reflection in a root vector of an integral lattice, it preserves the lattice and lattice norm
3h
answered Why is reflection in a plane an automorphism?
1d
comment Integer solutions to $\prod\limits_{i=1}^{n}x_i=\sum\limits_{i=1}^{n}x_i^2$
I am going out shopping for now. if you email me, I can send you the pdf as reply mail when I get back
1d
comment Integer solutions to $\prod\limits_{i=1}^{n}x_i=\sum\limits_{i=1}^{n}x_i^2$
Barak, You are missing that it has a superb answer published 100 years ago. Also I pasted in the page with Hurwitz' table of $n \leq 10.$ Where did you get your question, anyway?
1d
answered A circle in the plane contains at most four lattice points?
1d
comment Integer solutions to $\prod\limits_{i=1}^{n}x_i=\sum\limits_{i=1}^{n}x_i^2$
barak, it is more natural to allow a fixed integer coefficient in front of the product of the $x_i.$ See math.stackexchange.com/questions/1330482/… I also have a pdf of Hurwitz (1907), which is extremely well done.
1d
comment Integer solutions to $\prod\limits_{i=1}^{n}x_i=\sum\limits_{i=1}^{n}x_i^2$
your last line is incorrect, with the $n$ coefficient as in Hurwitz, there is always the solution $(1,1,1,1,\ldots,1).$ I have a pdf of Hurwitz (1907) if you would like to read it. It is really very well done, I gave only a small portion of it. My email address is now in my profile
1d
comment Are there infinitely many $k$ for which $\frac{\sigma(k)}{k}$ is a rational square where $ \sigma(k) $ and $k$ both are square?
hmmm... actually, Noam just says "perhaps this follows from known results" referring to there being infinitely many
1d
comment Are there infinitely many $k$ for which $\frac{\sigma(k)}{k}$ is a rational square where $ \sigma(k) $ and $k$ both are square?
see mathoverflow.net/questions/212517/… where Noam thinks it should be possible to prove something; and is the reason for this question being posted here. Note that the problem was attributed to Fermat by Jacques Ozanam, see pages 54-58 in volume I of Dickson's three volume History of the Theory of Numbers
2d
comment Question about the gradient of a function?
normal vector to a level curve, if in two dimensions. To a level surface, if in three
2d
revised What's the last whole number before a googolplex?
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