Jack M
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 Feb28 asked How is integer polynomial factorization reduced to factorization over a finite field? Feb26 revised How to visualize the Cartesian product of a set and an interval edited tags Feb26 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... Feb26 comment Find all integers $x$, $y$, and $z$ such that $\frac{1}{x} + \frac{1}{y} = \frac{1}{z}$ Indeed, it's equivalent. Feb24 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? Feb24 answered Meaning of derivatives Feb24 accepted False proof: no element has a prime norm in the ring $\mathbb Z[\zeta_p]$ Feb24 asked False proof: no element has a prime norm in the ring $\mathbb Z[\zeta_p]$ Feb24 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 $a^{p-1}\equiv 1$. Feb24 answered Variation of Fermat's little theorem Feb23 comment Algebraic maninpulation of formula to isolate a variable Why did you leave several answers? Feb23 revised Algebraic maninpulation of formula to isolate a variable deleted 269 characters in body Feb23 answered Algebraic maninpulation of formula to isolate a variable Feb18 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. Feb18 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? Feb18 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? Feb16 comment Proof of a Cayley graph result. Don't you think you should specify what $S$ and $G$ are? Feb16 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. Feb16 comment If $a^{-1}$ has a cube root, so does $a$. @Marko Exactly, although you might check that you can prove $(bbb)^{-1}=b^{-1}b^{-1}b^{-1}$. Feb16 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 $b^{-1}b^{-1}b^{-1}$?