Does anyone know a way to find integers a,b such that

Does anyone know a way to find integers a,b such that
gcd(a,b) > 1
gcd(a,b+1) > 1
gcd(a+1,b) > 1
gcd(a+1,b+1) > 1

I am having a hard time just producing one example.

Other urls found in this thread:

numbertheory.org/ntw/web.html
en.wikipedia.org/wiki/Topic_model
twitter.com/NSFWRedditVideo

Thanks for the pointers. In particular mention of representation theory reminds me of the Langlands conjecture. Might make that a goal or something
Not a bad idea. Just hope I don't have too many holes that I spend all my time on algebra

>In particular mention of representation theory reminds me of the Langlands conjecture. Might make that a goal or something
that would be a long term goal for sure, it's an incredibly vast web of conjectures but very interesting and lots of work to still be done. it would be good to learn some basic class field theory and modular forms first for motivation

do you think they exist?

How do you guys keep up with news in math and comp sci

I JUST found out that polymath brought down twin prime bound down to 246

I think so. I was given a problem where I have to prove an upper bound of a property of these numbers.

My first instinct was to find examples so that I could try to conjecture and generalize from there but I have been going for like 30 minutes and I have found no examples.

arxiv
numbertheory.org/ntw/web.html
tao's blog

you need to stop browsing Veeky Forums yesterday

find any yet?

look at Fourier Transform tables, first. Like spend 5 minutes in Wiki. Seriously. That's all it takes.

Digital filter design is pretty easy to accomplish with Matlab, if you have access to it and the DSP toolbox. I'm sure many user's here have that so if you want the filter coefficients, just tell them what type of filter you'd like and give some requirements and they'll fart you out some numbers for you.

Chemical nomenclature is not necessary info its just there for normies to feel like they can be smart because they memorized a bunch of labels. Real chemists just use the damn periodic table.

Anything sulfur containing, they all produce the same hydrogen sulfide compound that smells like rotten eggs.

EE is not a dying field. It will probably be a very lucrative field in the next 10 years in the US especially. Our company has many EE's nearing retirement that were trained during the advent of the cold war/nuclear submarine programs who are very talented and will need to be replaced with new blood.

First off, I'm under the assumption that terminals a and b are the terminals that are labeled as Vt+ and Vt- in the picture.

At DC, the impedance of the cap is infinite, making it an open circuit - so no current will flow along the top horizontal wire. Likewise, Vt is an actual open circuit, so no current will flow through it. Using Kirchoff's current law (KCL) on the node shared by Vt+, 1 Ohm, and the cap to know that there cannot be current flowing through the 1 ohm resistor. Now use KCL on the node shared by the cap, the 5ohm resistor and the dependent voltage source to know that there cannot be any current flowing through the 5 ohm resistor. Now that we know all the current amounts (aka - all are zero), we can use Ohm's law and Kirchoff's voltage law (KVL) to determine Vx.

Because there is no current flow in any portion of the circuit, there will be know voltage drops across any of the resistors. KVL then would tell you that 20/s = 0 V [ voltage drop across the 5 ohm resistor] + Vx. So, Vx = 20/s

tl;dr - yes.

Reactions tend to progress in the direction that is most energetically favorable, a condition that is expressed through the equilibrium constant. Everything from there is just le chatlier's principle which is basically if equilibrium is disturbed, the reaction will progress in the direction that reestablishes equilibrium (this includes heat, where exothermic reactions have heat as a product and endothermic have it as a reactant).

To all the analysts:
I realise that I need to use the intermediate value theorem to solve this, but choosing the interval (0,1) doesn't work. What would be a better interval to choose?

x=1/e

What kind of graph is this

It's from this en.wikipedia.org/wiki/Topic_model

I need some help understanding the sign convention on this optics problem.

So i have a person with bad eyesight 2cm from a lens, this person can see 300cm with relaxed eye and 150cm with strained eye.

I'm supposed to find the focal point for both, but I'm not sure if I just use the lens equation 1/f = 1/p + 1/q.

My p is 2cm, but what about my q for either one? Is the q negative for strained eye and positive for relaxed eye?

Is there any resource to seeing all the basic linear algebra theorems and definitions right in front of my face for studying?

It feels like I forgot the stuff I studied for the past exams, now finals are coming up. Anyone recommend a good cheatsheet-y resource?

Any tips and techniques? We're stepping into proofing stuff as well.

Thanks.

is anyone else not seeing latex? i read something about mathjax cdn shutting down but havent seen any posts about it

I want the following :
Start to care about myself
Achieve success
Stay healthy

This is my current situation:
I am out of jobs( getting rejected all the time unless it is about really low class job), clinging on a dead end job.
I am looking at other jobs to finance my student life.
I don't seem to care about my looks, I just let myself go although I still lift.
I am fat and live in a household inhabiting neurotic, toxic people who just mean well, although all it does is just hurt my self esteem.
I am depressed and on pills.
My situation frustrates me, but also I feel like it is too much a hassle to change it and I am too comfortable rotting in my comfort zone.

I don't know what else to add, please ask me questions, let me answer them and help me to help myself.

Good on ya for taking your meds.

Do you have people that you hang out with at school/other activities?

I used to live in a toxic household when I was getting my bachelors degree and what helped me was having a fun hobby where I could meet people. Contrary to what others say, lifting didn't help my mental state so I dropped it and joined my school's salsa/latin dance club, robotics club, and car club. I didn't make any close friends, but I made enough friends to go out clubbing and shit every now and then (which I enjoy as well). Be really nice with people and they might buy you drinks.

I guess my biggest suggestion to you is to get out of the house. Tell your family that you're going to study at school or something. Get your chores out of the way then gtfo of the house. That's what I wish I did when I was in your shoes. Things are better now, but I wish I did that more often.

Success is what you define it to be. My idea of success is living my life according to how I want to -- not my parents, not my siblings. Me. I dictate how I live my life. Sometimes I have days where I don't pick up after myself or skip the dishes and just eat take-out. But you know what? That's my fucking life and I love it. Find the life that you want. It's good that you know that you live in a toxic household, but you need to get out more to experience what more life has to offer.

It's hard to start caring about yourself when you've lived your whole life doing the opposite. But I'm sure you already do care about yourself, seeing as you're taking meds which I presume you got from a doctor. So you do care for yourself. It's hard to recognize, but you're on the right track, man. Treat yo self out every now and then. Leave the house whenever you feel like. Etc.

Good luck, man.

always use vector notation liek OA, since htey are singed, before using p and q

...

For a quadratic equation is easy to see that the difference of both roots is [math]x_2-x_1=\frac{\sqrt{b^2-4ac}}{2a}[/math]
Is there similar (simple) expressions for the difference of two roots of a cubic equation (of couse x_3-x_2 and x_2-x_1 are usually different)?

For polynomials up to degree 5 there are closed formulas for their roots.
So aside from the "simple" the answer is yes.

Matlab tells me that:
-(27*a^2*(((d/(2*a) + b^3/(27*a^3) - (b*c)/(6*a^2))^2 + (- b^2/(9*a^2) + c/(3*a))^3)^(1/2) - b^3/(27*a^3) - d/(2*a) + (b*c)/(6*a^2))^(2/3) - 9*a*c - 3^(1/2)*b^2*1i + 3*b^2 + 3^(1/2)*a^2*(((d/(2*a) + b^3/(27*a^3) - (b*c)/(6*a^2))^2 + (- b^2/(9*a^2) + c/(3*a))^3)^(1/2) - b^3/(27*a^3) - d/(2*a) + (b*c)/(6*a^2))^(2/3)*9i + 3^(1/2)*a*c*3i)/(18*a^2*(((d/(2*a) + b^3/(27*a^3) - (b*c)/(6*a^2))^2 + (c/(3*a) - b^2/(9*a^2))^3)^(1/2) - b^3/(27*a^3) - d/(2*a) + (b*c)/(6*a^2))^(1/3))
Is the (already simplified), result if you calculate the roots first 3 roots of the polynomial ax^3+bx^2+cx+d and calculate root2-root1.

You should take this with a grain of salt though, I (or even matlab) might have made a mistake

Should a Beer's Law plot always start from the origin?

There has to be an elegant way to write that as a function of the discriminant of the cubic equation, isn't it?

Is it possible that we can't comprehend anything faster than the speed of light and that anything moving faster than the speed of light can't aswell?

Possibly.
I have no Idea how to test that though.

>Is it possible that we can't comprehend anything faster than the speed of light and that anything moving faster than the speed of light can't aswell?
no.

The question is entirely pointless, if there is something that we can not possibly comprehend, then asking if it exist leads to absolutely nothing.

if your inside and can't see the sun, is the sun real, or just a thought with faith that reality is reality..???

Morally, what are ordered pairs in set theory?

The obvious answer would be "coordinates of a graph", but set theory has no notion of graph, and you can't put sets on an axis.
Since functions and relations are defined as sets of ordered pairs, is the ordered pair (a,b) supposed to represent the "arrow" from a to b? If so, how is that linked to the coordinate notion?

Is there any way to experimentally determine the resolving power or a grating-based spectrometer using a single laser (ie a single frequency), or is more than one frequency necessary?

The standard definition is that (a,b) := {{a},{a,b}}

It's nicer to think about ordered pairs in the fashion of some sort of "labeling" but this is circular because you need functions to label things, and functions need ordered pairs.

I doing a chemistry question, which was to find the empiracle formulae of an alcohol that has 64.9% carbon, 13.5% hydrogen and 21.6% oxygen by mass.

So far I've done all the calculations and I get:

C= 3.9
H = 9.6
O = 1

The problem is where to go from here. Those aren't intergers and the only interger I can multiply them by is 10, which gives me a silly chemical (C39H96O10 is not an alcohol). Should I just round up and call it C4H10O?

Thanks, but I don't think anyone disputes that the standard definition is completely arbitrary, in that there are other possible constructions that are equally consistent.

That's why I asked if there are any particularly [math]moral[/math] definitions, but I'm starting to think that the answer is negative, at least for set theory.
But I'm also currently reading about alternative foundations, and I do think Lawvere was on to something when he defined pic related using ordered pair notation: for example, an object of (f,g) can be interpreted as a formal assignment from an object of f to an object of g. Not sure how much mileage I can get out of this though.

I'm not sure what you want. You need some method of labeling elements 1 and 2 without using the numbers one and two because you haven't defined how to do that.
How would you expect it to not be somewhat arbitrary?

>categoryfaggot
Ah. It makes sense now.

A quiz question asked me to explain why my answer for part a (an ordered pair representing the minimum of a multi-variable function) "could not occur for a continuous function of one variable". My answer was "It is impossible to pass 2 arguments to a single-variable function, so my answer could not be used." I got no credit, with no explanation. How is this incorrect?

how do I show that

[eqn]\frac{k^{2}}{k^{3}-1} \geq \frac{1}{k} [/eqn]

k^2 >= k^2 - 1/k

so your focal point is always negative?

>Should I just round up and call it C4H10O?
Yes

What topic is a nice intersection of analysis and algebra?

calculus? Calc is elementary analysis, and algebra is a prereq for calc

I mean the abstract algebra kind of algebra.

Howabout discrete mathematics. Plenty of analysis, a good amount of algebra depending on where you look

hence the topic's inclusion in the stupid question thread. Did you forget where we are posting?

Your point is well taken but even you know that it can actually be useful to know certain ones off the top of your head if you use them regularly, my meme questions notwithstanding.

where can I find phase diagram for Fe-Mn-C ?

Let B be an odd integer.
Then (B-1) and (B+1) are even, and so
(B-1)*(B+1) is even. Assume
we can find an odd integer A
that divides (B-1)*(B+1). Set
a = (A+B)/2, b=(A-B)/2 and
k = A-((B-1)*(B+1))/A.
Then a+b = A while
4*a*b+1 = 4*(A+B)/2*(A-B)/2 + 1 =
A^2-B^2+1=A^2-(B-1)*(B+1)
= A* ( A- (B-1)*(B+1)/A )
= (a+b)*k
which is dividble by (a+b).

Example: Take B=13. Then (B-1)*(B+1)=168
=8*21, and we can take A=21. Then
a=(A+B)/2=17, b=(A-B)/2=4,
k=21-8=13. Check:
(4*17*4+1)/(17+4)=13.

Note (B-1)*(B+1) will be divisible by an odd number A>1 unless (B-1)*(B+1) is a power of 2, i.e. unless (B-1) and (B+1) are powers of 2, i.e. unless B=3. If B=3, can take A=1.