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Sep
26
comment Nice Question in Mathmatics about Times
In $47^{74}$ hours we will be in the grave. Whoever set that problem should have made at least a mild effort to keep the premise from being completely ridiculous.
Sep
25
comment Is there a group between $SO(2,\mathbb{R})$ and $SL(2,\mathbb{R})$?
I made an error in my previous comment, so I deleted it.
Sep
25
answered What does the class number tell us about a quadratic form?
Sep
20
comment Mordell Diophantine: $x^2+11=y^3$
@MarkFischler, what are some rings that you know how to show are UFDs already, and by what methods? (Not by a long shot can you replace 11 with any positive $4m+3$ and expect to have a UFD.)
Sep
19
comment Mordell Diophantine: $x^2+11=y^3$
The UFD method does work, but you need to be in the UFD $\mathbf Z[(1+\sqrt{-11})/2] = \{(a+b\sqrt{-11})/2 : a \equiv b \bmod 2\}$, not in the non-UFD $\mathbf Z[\sqrt{-11}]$. The usual method shows $x+\sqrt{-11}$ is a cube in $\mathbf Z[(1+\sqrt{-11})/2]$, so you can write it as $((a+b\sqrt{-11})/2)^3$, where $a \equiv b \bmod 2$. Comparing coefficients of $\sqrt{-11}$, $1 = (3a^2-11b^2)b/8$. If $a$ and $b$ are even then $a = \pm 4$ and $b = 2$, leading to $x = \pm 58$ and $y = 15$. If $a$ and $b$ are odd then $a = \pm 1$ and $b = -1$, leading to $x = \pm 4$ and $y = 3$.
Sep
18
comment If $f(x+a)$ is irreducible over $F$ then $f(x)$ is irreducible over $F$
There really are situations where it is easier to prove $f(x+1)$ is irreducible, and then this result shows $f(x)$ is irreducible too. The simplest family of examples is $(x^p-1)/(x-1)$ in $\mathbf Q[x]$, where $p$ is a prime number.
Sep
13
comment Examples of falsified (or currently open) longstanding conjectures leading to large bodies of incorrect results.
Typo: the $2n-2$ in the excerpt should be $2^n-2$.
Sep
13
comment Examples of apparent patterns that eventually fail
The number 256 is the wrong power of two for the obvious pattern with $n < 5$ to continue at $n = 10$.
Sep
12
answered What are some examples of induction where the base case is difficult but the inductive step is trivial?
Sep
12
comment How to endow topology on a finite dimensional topological vector space?
@MarianoSuárez-Alvarez: the possibility that the field is something other than the real or complex numbers is not more or less a pathology. The result is also true for vector spaces over the $p$-adic numbers. Of course in the context of Conway's book, only the real and complex numbers were intended.
Sep
12
comment Examples of apparent patterns that eventually fail
@saadtaame: Such examples are found using resultants and factoring polynomial a mod $p$. See the top answer at mathoverflow.net/questions/130783/… for a similar example.
Sep
11
comment “Bad” primitive root $\bmod p^{2}$
You are not using the terminology from that link correctly. The term used there is "bad primitive root", and in any case it means something different from what you wrote: the first condition should not be $m^{p-1} \equiv 1 \bmod p$, but rather that $m \bmod p$ is a primitive root. All $m$ not divisible by $p$ satisfy your first condition, which is a lot weaker than being a primitive root mod $p$.
Sep
10
comment Rational equality modulo $p$
Using the term "for almost all" does not clarify as much "for all but finitely many" would.
Sep
10
comment Rational equality modulo $p$
Asking for something not to hold for large $p$ and then saying that in particular it should hold for infinitely many $p$ sounds like there is a typographical error; "not all large $p$" does not imply "infinitely many $p$," so could you please say more clearly what sets of $p$ you do want this to hold for?
Sep
10
asked How are Sudoku puzzles created?
Sep
7
comment Help with Conrad's “Recognizing Galois Groups”
@ErikVesterlund: I've updated the file, so it should be clearer now (although Pete's answer may already have explained what you wanted).
Sep
6
comment Differentiation Proving
"... and provide all the steps". You want other people to completely do your work?
Sep
1
comment Prove that a norm makes a space Banach
@Freeze_S: Oh, I see. I was unaware of that (I don't work on C*-algebras).
Sep
1
comment Terminology for Galois groups of non-Galois extensions.
If you are seeing this somewhere, it would be useful if you gave an excerpt for context.
Sep
1
revised What is the use of scheme theory?
edited body