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Feb
28
asked How is integer polynomial factorization reduced to factorization over a finite field?
Feb
26
revised How to visualize the Cartesian product of a set and an interval
edited tags
Feb
26
comment Why is Gödel's Second Incompleteness Theorem important?
Sure, trusting $T$ because $T'$ says it's consistent is not epistemologically sound, but is trusting $T$ just because it can prove itself consistent any better? Is that not some form of circular reasoning? Self-proving consistency has the advantage of being amenable to a precise mathematical definition, but that doesn't necessarily make it philosophically useful...
Feb
26
comment Find all integers $x$, $y$, and $z$ such that $\frac{1}{x} + \frac{1}{y} = \frac{1}{z}$
Indeed, it's equivalent.
Feb
24
comment Is it ever easier to show differentiability than continuity?
In order to even take a partial derivative, you have to show that $f$ with one variable fixed is a continuous function (in fact, that it's a differentiable function). So perhaps a good question to ask is: what kind of function is obviously continuous when one variable is fixed, but not obviously continuous in both variables?
Feb
24
answered Meaning of derivatives
Feb
24
accepted False proof: no element has a prime norm in the ring $\mathbb Z[\zeta_p]$
Feb
24
asked False proof: no element has a prime norm in the ring $\mathbb Z[\zeta_p]$
Feb
24
comment Variation of Fermat's little theorem
@Broly A primitive root modulo $p^2$ by definition has the property that $p(p-1)$ is the smallest exponent making it congruent to $1$, but the definition of $a$ was that $a^{p-1}\equiv 1$.
Feb
24
answered Variation of Fermat's little theorem
Feb
23
comment Algebraic maninpulation of formula to isolate a variable
Why did you leave several answers?
Feb
23
revised Algebraic maninpulation of formula to isolate a variable
deleted 269 characters in body
Feb
23
answered Algebraic maninpulation of formula to isolate a variable
Feb
18
comment Have to use pythagoras theorem
Are you sure you're supposed to use the Pythagorean theorem? It's not what I'd use for this problem.
Feb
18
comment Evaluate $\frac{x^3-x^2-5x-3}{x^3-x^2-15x} \ge 0$
Those are the values at which the function equals zero. Is that what you're interested in?
Feb
18
comment Evaluate $\frac{x^3-x^2-5x-3}{x^3-x^2-15x} \ge 0$
What do you mean $x=3$ and $x=-1$? The function is $\geq 0$ in between those values?
Feb
16
comment Proof of a Cayley graph result.
Don't you think you should specify what $S$ and $G$ are?
Feb
16
comment How to find all the $x$ values such that $x^2 = a \mod n$
Wikipedia is a poor resource for quadratic reciprocity and related theorems. Find yourself a book on number theory. Ireland and Rosen's Classical Introduction covers QR. There is also an english translation of Gauss's Disquisitiones, which remains a good and readable introduction to the subject to this day, although the QR stuff is buried a couple of chapters in.
Feb
16
comment If $a^{-1}$ has a cube root, so does $a$.
@Marko Exactly, although you might check that you can prove $(bbb)^{-1}=b^{-1}b^{-1}b^{-1}$.
Feb
16
comment If $a^{-1}$ has a cube root, so does $a$.
@Marko As soon as you got to $a=eee$ you should have spotted a big, big problem - $eee$ is $e$, so you've just said that any element whose inverse has a cube root is the identity! I actually can't pinpoint where you went wrong because at the point where you have the $\to$ sign you seem to have done about five things at once. I agree that $baa^{-1}b^{-1}=e$, but why do you claim that the left hand side equals $b^{-1}$? Furthermore, what does that have to do with $a$ being equal to either $eee$ or $b^{-1}b^{-1}b^{-1}$?