One Of The Worst Parts About Being A Mathematician Is That Sometimes Your Working On A Project That Is

Yes.

Suppose 2n/(n-2) is an integer. Call it k. Then 2n = (n-2)k. But notice also that (n-2)×2 = 2n-4. So 2n is divisible by n-2, and so is 2n-4. So their difference, 4, is also divisible by n-2.

(

To see this, subtract the two equalities above. You'll get 2n - (2n-4) = (n-2)k - (n-2)×2, or, simplifying, 4 = (n-2)(k-2), so 4 is divisible by (n-2)

)

The only (positive integer) factors of 4 are 1, 2, and 4. So n-2 has to be 1, 2, or 4, and thus n has to be either 3, 4, or 6.

The question asks only for positive integers, but it would be a mistake to exclude the negatives. If we take negatives into account also, then -4, -2, and -1 also work, for which we get n to be -2, 0, and 1. And notice here that 1, although reached via a negative, is in fact a positive integer solution.

So the only numbers are 1, 3, 4, 6.

For more information on this, this kind of question comes under a part of math called Number Theory.

Does anyone know if 3, 4, and 6 are the only positive numbers for which 2n/(n-2) is an integer or are there more?

REBLOG THIS POST IF YOU ARE A MATH ENJOYER

No it is not optional, I desperately need to follow y’all so that there is more math on my dashboard.

when you are a child, you solve equations. we grown-ups have to solve inequalities.

Heartbreaking! The obvious letter to use for this variable isn't available because you already used it for something else!

Getting a lot of: “No but like you don’t get it math is stupid and useless and reading books is actually morally good… and teaches us about the world around us and explains how it works which stupid math doesn’t do why should I learn calculus I would rather shame people into reading Jane Eyre than open a math book or website”

And like … out of the millions of things you can do with basic and foundational math … that shows you how the world works … Calculus, as one example, can literally explain to you why leaves grow at the angle they grow … there is little more beautiful than being able to calculate exactly how nature works and understand why.

There is beauty in every subject … and few other subjects encapsulate ways to understand your surroundings like math.

If you are comfortable shaming people for not reading fiction books because you personally are good at reading them, but uncomfortable being shamed for not doing mathematics consider you are in the exact same boat as people who are afraid to read fiction books because they don’t see why it is important to do so and are unwilling to begin.

You are the people you hate.

What kind of math are you studying?

math tuition is hell im gonna shoot myself with a gun

Me and my best friend

mathematics/art

i hate when i browse math-related tags on this site and half the posts are people ranting about how much they hate her. why are you so mean to my wife

Euclidean Geometry in Mathematical Olympiads

Geometric proofs… might anyone have a good resource for learning them more formally? I need them for a project I’ve recently begun, and hope to find a guide stronger than those reserved for high school geometry courses haha.

Specifically, i’m looking to understand lines, line intersections, things of that type, in a deeper way.

Thank you! :)

A lot of people absolutely fail to distinguish between 'I hate this because I was taught this badly' and 'I hate this because this thing is inherently bad', and I hate it.

you know I absolutely agree with the fact that the education system is fucked and traumatises students. I absolutely agree with the fact classes like english and maths and history can be piss boring and teach you nothing of worth and could be a trigger depending on how hellish of a teacher you were given.

Hell, the only reason I love maths is because I primarily engaged with it outside of class and found it fun on my own terms. I'm still bitter towards my history teachers for having clear favourites and not engaging half the class.

but like. if you're railing against the *subjects* themselves, refusing to learn any of the basics as an adult, and bringing up how much you hate them at every opportunity? At some point that becomes a problem you have to deal with yourself.

and if you don't, you're going to be the reason this happens again for the next generation.