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2h
comment integrating non functions
Are you still here?
1d
comment Quadratic Extensions
No, you won't find a polynomial in a field. And if $a$ is in $F$ (as it says in the problem), then the minimum polynomial for $a$ is just $x-a$.
1d
comment Find the lowest value of $x$ so that $x \in (A \setminus B)$
If $x$ is to be a positive integer, then it can't get any smaller than 1, and, since 1 is prime to 12 and is not prime, it must be the answer. My guess is that it's not the answer intended by the person who set the problem. I bet that person had 25 in mind as the answer. But the way you have posed the question, it has to be 1.
1d
comment Find the lowest value of $x$ so that $x \in (A \setminus B)$
Actually, $-1001$ is relatively prime to 12, and is not a prime, and is lower than 25 (and also lower than 1), so it's a better answer than either of those. Of course, $-10000001$ is an even better answer, and $-100000000001$ is better still.
1d
comment integrating non functions
No, it doesn't make any sense to integrate $x^2+(y-1)^2=1$. One integrates functions, not equations. Now, $x^2+(y-1)^2=1$ does define $y$ as a function of $x$, since it is equivalent (if you assume, say, $y\ge1$) to $y=1+\sqrt{1-x^2}$, and you can do $\int(1+\sqrt{1-x^2})\,dx$. Also, it makes sense to integrate some function $f(x,y)$ along the curve defined by $x^2+(y-1)^2=1$. Does either of those interpretations seem like what you had in mind?
1d
answered Set of all integer solutions to a linear diophantine equation
1d
comment The Coin-Exchange Problem (Application of the Residue Theorem)
That's a lot of work you are expecting someone to do. Much better to 1) show us how much of it you can do yourself, 2) ask one simple question about how to take the next step after you get stuck, 3) when you get an answer you understand, go back to the problem to see how much further you can get, 4) if you get stuck again, ask one more simple question, 5) iterate until you can do the whole problem.
1d
revised Quadratic Extensions
typo in title; edited tags
1d
comment Quadratic Extensions
The problem says $a$ is in $F$. $F(\sqrt a)$ is the smallest field containing both $F$ and $\sqrt a$, which is $\{\,r+s\sqrt a:r,s{\rm\ in\ }F\,\}$.
1d
comment relation between trace of product and sum of matrices?
In the scalar case, there's the inequality of the arithmetic and geometric means, $\sqrt{xy}\le(x+y)/2$.
May
22
comment How to find minimal polynomial of primitive element (field theory)
No, the minimal polynomial for $\gamma$ is the monic polynomial $p$ of smallest degree such that $p(\gamma)=0$.
May
22
comment How to find minimal polynomial of primitive element (field theory)
Sorry, I meant, if you let $\beta=\alpha^7$ (so $\beta$ is the element for which you want the minimal polynomial), then $\beta^9=1$.
May
22
comment Prove that there is a real number $a$ such that $\frac{1}{3} \leq \{ a^n \} \leq \frac{2}{3}$ for all $n=1,2,3,…$
Do you have some reason to believe that it is true?
May
22
comment How to find minimal polynomial of primitive element (field theory)
Do you see that $\alpha^9=1$?
May
22
revised hexagonal tessellation (tiling): uniform distribution of centers of hexagons?
typos in title
May
21
comment Reference for measures of commutativity needed
Now posted to MO, without notifying either site: mathoverflow.net/questions/207126/…
May
21
comment Combinatorial optimization problem
You must use $a_1V_1+a_2V_2$ for some $a_1$, $a_2$ satisfying $0\le a_1\le V/V_1$, $0\le a_2\le V/V_2$, so there are only finitely many possibilities you have to test.
May
20
comment $ x^2+y^2+z^2=k(xy+yz+zx) $
What then? Three examples?
May
20
comment $ x^2+y^2+z^2=k(xy+yz+zx) $
"Some examples say yes...." How many examples? A thousand? A million? Is there a proof written down somewhere that there are no nontrivial solutions for $n$ in those sets? Is there a proof that there's a solution, if you don't restrict to positive integers? The more you tell people, the easier it will be for someone to help you.
May
20
comment $ x^2+y^2+z^2=k(xy+yz+zx) $
Strange collection of conditions. Have you tested this for all $n$ up to whatever? Where does this question come from?