Discovering Something New In Mathematics And Then Naming It After Euler Just To Fuck With People.

What kind of math are you studying?

math tuition is hell im gonna shoot myself with a gun

You took this photo? I've loved it for a long time!

when people are like “he’s not even attractive you could find a guy that looks like him at any gas station” i’m like….. well you see there’s beauty everywhere actually

born to go to beautiful libraries and study, forced to hustle in my room <3

Also Griebach, known for the Griebach Normal Form!

Discover that a name you’ve been hearing for years belongs to a woman! (shout out Phyllis Nicolson of Crank-Nicolson method fame)

The cool thing about category theory is that a lot of times I can forget a definition, just think for a minute about what it "should be", and then when I go and look it up I'm right. I've experienced this to a lesser degree in other areas of math but in category theory it seems to come particularly easily.

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

mathematical revelation so great i almost became religious

reading math textbooks means getting insane whiplash when you read the notes in the margins

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.

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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?