• Yesterday, 04:59
Joseph A. Gallian, in his book, "Contemporary Abstract Algebra" (Fifth Edition) defines an irreducible element in a domain as follows ... (he also...
0 replies | 34 view(s)
• Yesterday, 04:23
Thanks for the help johng ... But i am still a bit puzzled ... I think we have to show that \{ \frac{k}{ 2^n} \ | \ k.n \in \mathbb{Z} \} is...
3 replies | 51 view(s)
• Yesterday, 02:29
MarkFL replied to a thread 231.14.88 3d surface in Calculus
Multiplying through by $9+6x-8y$ and distributing the $26$, we obtain -x^2-y^2+z^2=156x-208y+234 -x^2-156x-y^2+208y+z^2=234 ...
3 replies | 53 view(s)
• February 17th, 2017, 07:04
$hint:$ $if \,\,a=1\,\, then \,\,b=?$ $if \,\,a>1\,\, then \,\,no \,\,solution.\,\, why ?$
1 replies | 77 view(s)
• February 16th, 2017, 23:12
I am reading Stephen Lovett's book, "Abstract Algebra: Structures and Applications" and am currently focused on Chapter 5 ... I need some help...
3 replies | 51 view(s)
• February 16th, 2017, 07:22
\ The roots are reciprocals, because the left hand side of $(1)$ is symmetric in $x$ and $\frac{1}{x}$, so both roots yield the same RHS, namely...
3 replies | 123 view(s)
• February 15th, 2017, 20:29
You have two points on the graph, so you can compute the slope as follows: m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} Then, you can...
2 replies | 58 view(s)
• February 14th, 2017, 23:47
Yes, the derivative of the function evaluated at the $x$-coordinate of the tangent point will give you the slope $m$ of the tangent line. :)
4 replies | 89 view(s)
• February 14th, 2017, 23:18
The first derivative of a function gives you the slope of the tangent line, not the tangent line itself. Thus,for some function $f(x)$, the tangent...
4 replies | 89 view(s)
• February 14th, 2017, 22:17
Let's try your substitution of: u=x+9\implies du=dx I=\int_9^{18}\frac{(u-9)^3}{u^2}\,du By the binomial theorem: ...
1 replies | 47 view(s)
• February 14th, 2017, 22:14
$a,b\in N$ $k=\dfrac {ab^2-1}{a^2b+1}\,\, \,also \,\,\in N$ find pair(s) of $(a,b)$
1 replies | 77 view(s)
• February 14th, 2017, 22:01
$\sqrt {x+\dfrac {1}{x}+1}+\sqrt {x+\dfrac {1}{x}}=x$ find the value(s) of $x$
3 replies | 123 view(s)
• February 14th, 2017, 12:31
Just to follow up, we left off with: 8-\frac{15000}{x}=5 Arrange as: 3=\frac{15000}{x} Multiply through by \frac{x}{3}\ne0:
2 replies | 100 view(s)
• February 14th, 2017, 10:52
$x,y\in N$ $\dfrac {1}{x}+\dfrac {1}{y}=\dfrac {1}{2010}---(1)$ How many pairs of $(x,y)$ we may get to satisfy (1)
2 replies | 98 view(s)
• February 12th, 2017, 22:13
Thanks for the help, Euge ... Appreciate your assistance ... Peter
2 replies | 61 view(s)
• February 12th, 2017, 16:23
Hello!!! (Wave) I am reading about the Method of Four Russians from here. We divide the dynamic programming table $D$ into $t$-blocks such...
0 replies | 35 view(s)
• February 12th, 2017, 03:00
I have been thinking around the definition of a unit in a ring and trying to fully understand why the definition is the way it is ... ... Marlow...
2 replies | 61 view(s)
• February 12th, 2017, 00:21
Yes, we use $\LaTeX$ powered by MathJax, which is what you'll find on most other math sites. The only difference is, unlike other sites, we provide...
3 replies | 105 view(s)
• February 10th, 2017, 11:34
Let's generalize the method I posted >>>here<<< to reflect a given point $(a,b)$ about the line $y=mx+k$, where ($m\ne0$). We will call the reflected...
3 replies | 112 view(s)
• February 10th, 2017, 10:27
MarkFL replied to a thread Line y = (x/2) + 3 in Pre-Calculus
Another way to show 3 points are collinear is to pick two distinct pairs from the 3 points, and show that the slope between both pairs is the same. :D
2 replies | 55 view(s)
• February 10th, 2017, 00:30
MarkFL replied to a thread Square root Convergence in Calculus
To extend the ladder for $\sqrt{k}$, you want: x_{n+1}=x_n+y_n y_{n+1}=x_{n+1}+(k-1)x_n
1 replies | 73 view(s)
• February 9th, 2017, 15:50
Now necessarily...for example if we multiply through by $k$, we get: k+1=k^2 And BOOM! we have question 1 of part B) done.
12 replies | 187 view(s)
• February 9th, 2017, 08:36
Does anyone know of a book or web page that gives a history of the concept of a module and the history of modules in algebra ... i have not not...
0 replies | 31 view(s)
• February 9th, 2017, 03:49
We don't need to solve for $y$. We need only to have shown that: \frac{x}{y}=\frac{1+\sqrt{5}}{2} to satisfy part A) of the problem. For part...
12 replies | 187 view(s)
• February 9th, 2017, 02:15
That's not quite right: x=\frac{-(-y)\pm\sqrt{(-y)^2-4(1)(-y^2)}}{2(1)}=y\frac{1\pm \sqrt{5}}{2} Discarding the negative root, we obtain: ...
12 replies | 187 view(s)
• February 9th, 2017, 00:25
To solve for $x$ here, we let: a=1 b=-y c=-y^2
12 replies | 187 view(s)
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I know a thing or two about topology. Find number theory interesting but don't know much about it.
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Some of my notes on number theoretic topics are on a few primality tests and on Hardy & Littlewood's result (incomplete). The other articles are on quintics : about a brief description of Kiepert algorithm and a short introduction on quintic-solving algorithms, respectively. I have also written up an introductory thread on Riemann Hypothesis

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