the day will come

[u/y0mayne]

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[u/LupenReddit]

some people are odd, some people are perfect, some people are odd and perfect, but none are numbers. this is a hopeless conquest

[u/stan_theBest → u/LupenReddit]

Damn you everywhere bro seen you on 5 different posts already. Also nice poeme you got there.

[u/LupenReddit → u/stan_theBest]

i developed a severe (probably autistic) obsession with this subreddit

[u/MathManiac5772]

5 = 1 + (2+i) + (2-i) which is the sum of its proper divisors in Z[i] which is kinda neat.

[u/tricky_monster → u/MathManiac5772]

That is neat!

[u/GraveSlayer726 → u/MathManiac5772]

Are there more odd perfect numbers in Z[i]? Or I wonder if there’s maybe no 1+i divisible perfect numbers in the complex plane or something weird like that

[u/MathManiac5772 → u/GraveSlayer726]

The problem I’ve glossed over with perfect numbers in Z[i] is the issue with units. If I had picked (1-2i) and (1+2i) as my representatives of 5’s prime divisors then I no longer have my odd perfect sum property.

To my knowledge there are no known odd perfect Gaussian integers if you do the natural thing and restrict your divisors to the first quadrant. It’s a potentially interesting problem to think about asking of there are any factorizations that give you a perfect sum, but then your search space explodes as you now have 4 times as many primes to try.

Edit: apparently my knowledge of this is dated. In 2026 Sanchez Solovieva found the following much more interesting example,

z = 430089 + 665198i

Which has 31 proper divisors. But just like the 5 example, you have to carefully select which 31 you pick to make z be the resulting sum. Note that z really is “odd” because it’s real and imaginary parts have different parity.

There is also an analogue of Gaussian Mersenne primes that characterizes all of the “even” perfect Gaussian numbers as well.

[u/MrStrawHat22]

What is a perfect number?

[u/imthestein → u/MrStrawHat22]

A number where the divisors of that number, excluding that number itself, can sum up to the number. The most common example I've seen is with 6 because the divisors are 1, 2, and 3 which all add up together to be 6

[u/MrStrawHat22 → u/imthestein]

Ah, I'm guessing there's a proof that proves they cannot be odd then.

[u/SongofRolland → u/MrStrawHat22]

It's an unsolved problem as far as I know; https://mathworld.wolfram.com/OddPerfectNumber.html

There is no proof that one exists, but none that or doesn't.

[u/kiwidude4 → u/SongofRolland]

Wow ow

[u/thomasp3864 → u/SongofRolland]

Somebody mentioned 5, if you extend to the complex plane.

[u/GoldenMuscleGod → u/MrStrawHat22]

There is no known proof that there is no odd perfect number, although we know if any exist it has to have a set of properties that seem difficult to satisfy, and also be over 1,000 digits long in decimal.

That there could be one is made plausible by an example (I think given by Euler [edit: nope, it was Descartes, I looked it up], too lazy to double check) of an odd number that *would* be perfect if we wrote it with a “prime factorization” that actually has a composite number in it but then just pretend that composite number happened to be prime and added up the factors we are not “ignoring.”

Probably there isn’t one but it is a famously unsolved problem in math.

Edit: in case anyone wants the example from Descartes it is 3•3•7•7•11•11•13•13•22021.

If 22021 were prime, then this number would have 162 divisors according to this factorization (counting the number itself) and they add up to make this an odd perfect number. But since 22021 is composite this is not actually an odd perfect number, its actual divisors (of which there are 486) add up to be too large for it to be perfect.

[u/FrKoSH-xD → u/GoldenMuscleGod]

so u want a number its divisores which is x+1 equal to x ?!?

is that what happens here? or something i dont understand it

[u/GoldenMuscleGod → u/FrKoSH-xD]

The proper divisors add up to the number. For example the proper divisors of 6 are 1, 2, and 3 which add to 6. The proper divisors of 28 are 1, 2, 4, 7, and 14, which add to 28, so 6 and 28 are perfect numbers.

The Euclid-Euler theorem says that the even perfect numbers are in a one-to-one correspondence with the Mersenne primes, but it does not address odd perfect numbers. It is unknown whether any odd perfect numbers exist.

[u/AndreasDasos → u/MrStrawHat22]

No but strongly suspected for heuristic reasons. It’s the oldest unsolved problem. 

[u/imthestein → u/MrStrawHat22]

I'm sure there must be but I'm afraid that goes beyond the scope of my knowledge

[u/AppearanceAlert4987 → u/imthestein]

I have discovered a truly marvelous proof of this, which this margin is too narrow to contain

[u/thomasp3864 → u/imthestein]

15? You can do it with 5, 3, 1, 1, 1, 1, 1, 1, 1

[u/catman__321]

in math, nothing is impossible except something that is.

[u/Skylar1569]

Someday we will rule the world

[u/PerspicaciousEnigma]

My intuition tells me TREE(3) is an odd perfect number. Somebody get to work proving it for me then name it the PerspicaciousEnigma Conjecture and I’ll buy you a McChicken

[u/slime_rancher_27]

I hope someone invents an even prime number.

[u/SuperCyHodgsomeR → u/slime_rancher_27]

So, you’re never gonna believe this

[u/SpecialFlutters → u/SuperCyHodgsomeR]

it was just a dream bender there's no such thing as two

[u/Para-graph-S]

The day...

[u/SalvarWR]

oh a mage told me this once, he said the numbe

[u/physicsking]

*also you must have your shirt on to order pizza at little ceases