7h
comment Does there exist a unital ring whose underlying abelian group is $\mathbb{Q}^*$?
What do you mean by compatible? Seriously, just say what you mean!
11h
comment Multiplicative structure without unique prime factorisation
An element is prime if $p\mid ab\Rightarrow p\mid a$ or $p\mid b$. An element is irreducible if it has no factorization into a product of more than one noninvertible element. In the set of naturals with residue $1$ mod $3$, the element $4$ divides $10\cdot10$ but doesn't divide $10$, hence $4$ is not prime in this structure. You are talking about irreducible, not prime. This is understandable since we usually define prime numbers as irreducible natural numbers before exposing students to the more advanced, separate definitions.
18h
comment How do you find the square root of a binomial?
en.wikipedia.org/wiki/Binomial_series
Dec
15
awarded  Enlightened
Dec
15
awarded  Nice Answer
Dec
14
comment Why is this $6!$ factorial and not $p(6,1)$?
p(6,1) is the number of ways to arrange 1 out of the 6 candidates. An election in which only one out of the six candidates ever gets their name printed on a card would be a joke. Note further that you should be able to write down much more than 6 ways to arrange 6 names, with no real effort right off the top of your head. This should be obvious! Hell, 6 is the number of ways you can arrange just three names. By definition, the number of ways to arrange $k$ out of $n$ possible things in some order is $p(k,n)$; here $k=6$ and $n=6$.
Dec
13
comment show a group with prime order product is solvable
Have you tried to deduce anything whatsoever? What kinds of things do we normally do with arithmetic and the order of the group, or at least try to see if we can do?
Dec
13
comment Every infinite abelian group has at least one element of infinite order?
Don't "search" for one; make one yourself!
Dec
13
comment Sum of odd numbers is odd if each of the natural numbers is odd
"Sum of odd numbers" (in your title) does not mean "sum of an odd number of natural numbers" (which is the real question). Why are you writing $\sum_{i=1}^\infty i=2n-1$; what purpose does it serve? How are you trying to use induction? Why do you think $2(n+1)-1$ is even?
Dec
12
comment Why can a matrix whose kth power is I be diagonalized?
Second question: Have you tried computing powers of matrices of that form to tease out a pattern?
Dec
11
comment Why $\mathbb{Z}/n\mathbb{Z}$ isn't a subgroup of $\mathbb{Z}$
$\Bbb Z/n\Bbb Z$ isn't even a subset of $\Bbb Z$. More importantly, how many integers do you know in $\Bbb Z$ that return back to $0$ if you add it to itself enough times?
Dec
11
comment $\cosh(iz) -\cosh(z)=0$
@dustin $\cosh(iz)=\cos(z)$.
Dec
11
comment On the problem of polynomial bijection from $\mathbb Q\times\mathbb Q$ to $\mathbb Q$
I have voted to reopen. This question strikes me as the type for which, if someone was knowledgeable enough to answer, they could do so relatively easily, and within a fraction of the character limit for answers.
Dec
11
comment On the problem of polynomial bijection from $\mathbb Q\times\mathbb Q$ to $\mathbb Q$
@RghtHndSd I have seen topics which have entire books about them, that are bigger and more famous than this problem (e.g. stuff related to the Riemann zeta function), yield excellent answers on this site surveying the topic. Let's say every page worth of condensed, survey exposition covers the same amount of material as a couple dozen pages of detailed writing. Have you personally come across five hundred pages worth of material on this single question that I hadn't even heard of before seeing it here? It's possible I suppose, but when you begin your comment with "it seems," I am skeptical.
Dec
10
comment Could this discrete logarithm problem be proved?
Your first problem is determining if $X$ is a power of $A$. Your second problem is literally the same exact problem but with potentially different values of $X$ and $A$. There's no reason to have two copies of the same problem!
Dec
10
comment Rapid decay times polynomial decay is L^1?
(Polynomials don't decay, they grow.)
Dec
10
comment Could this discrete logarithm problem be proved?
There's no reason to copy-and-paste the problem into two copies of the same problem. Your real problem is determining when $X$ is a power of $A$ mod $p$. This is true if and only if the multiplicative order of $X$ divides the multiplicative order of $A$, if you're interested.
Dec
10
comment What is the sum of a finite series when the variable is in the denominator?
If I was playing around with a complicated expression with unknowns $x_1,\cdots,x_n$ and obtained that, I would consider it closed form and feel satisfied.
Dec
10
awarded  Caucus
Dec
7
comment $G/Z(G)$ is cyclic useful for proving groups abelian?
Usefulness is irrelevant. It's a test of students' ability to use tools they've been given.