algebra question

[warm temple]

how do you factorize equations in the form a^n + b^n ?

like for n = 2 you have (a + b)^2 - 2ab
and then for n = 3 you have (a + b)(a^2 - ab + b^2)
but like those two i know purely from memory

[native whale]

Oh hi PB

[warm temple]

hiii

[native whale]

I don't think there is a closed form for a^n+b^n tho

[warm temple]

Omg great pfp

[warm temple]

omg rlly :(

[native whale]

you too xD

[native whale]

yeah...

[warm temple]

noooooo

[native whale]

any degree more than 3 you might have to factor yourself

[warm temple]

i see, how would i approach doing that ?

[frozen temple]

consider visiting this MSE post.

[warm temple]

ill have a look rrn ty

[native whale]

Oh

So there are for n is odd

Make sense

[warm temple]

wow this looks really handy

i dont understand summation notation just yet but i will look back at this post asap once ive learnt some

[frozen temple]

yeah. for even n there are no real roots anyway.
I suppose for n >= 4 you can factor it into irreducible quadratics, but I have yet to see the formula for that, nor have I worked it out.

[native whale]

Yeah thought of that, I'm surprised it has a closed form for n odd tho

Since I never use them

[frozen temple]

I think this formula (or a^n - b^n, I forgot which) comes up often when talking about roots of unity.

[native whale]

You're smart PB, you got this

[native whale]

they don't even teach roots of unity here, but I do know a^n-b^n

I learnt something new today ty

[frozen temple]

well that only matters if you're learning complex numbers.