does this work

[hard loom]

I'm trying to prove that every odd int is the diff of 2 squares

[sturdy ember]

wait the calculation is incorrect, what happened from the first to the second line?

also 3≠√7

[hard loom]

Thanks for catching that

But it the idea sound

[sturdy ember]

and I think you meant difference of 2 squares of integers

right?

[hard loom]

Yea where k is a positive int

[sturdy ember]

oh sorry didn't see

[hard loom]

It's all good I didn't see my mistake in line 2

[sturdy ember]

wait what

k^2-k^2

that's obviously 0 right

[hard loom]

I mean I never said k had to be the same number

[sturdy ember]

yeah lemme quickly find a proof

[limber turtle]

what?

[brisk cloak]

???

[sturdy ember]

huh?

[limber turtle]

k has to be the same number

hence why you use the same letter

[hard loom]

I see

[limber turtle]

if it is a different number, then you should use a different letter

[sturdy ember]

do people throw their brain away when they get into uni or smt

[hard loom]

Ight sorry this is my first proof class

[hard loom]

I'd have to have one to begin with

[limber turtle]

no worries g

[sturdy ember]

no worries

[hard loom]

So something more like a^2 - b^2 = k+1

[sturdy ember]

yep

actually contradiction might be easier

lemme get some scrap paper

[hard loom]

Can't it has to be direct

[sturdy ember]

uh if that's what you prefer

but contradiction is chad

[hard loom]

No I wanted to do a different method

But that's not the assignment

[sturdy ember]

on second thought

direct is easier

yep yeah

[hard loom]

I worked it out to being a = sqrt(b^2 +k+1

Does that work as a end proof

[sturdy ember]

if you can discuss how "a" is an integer, yes

[sturdy ember]

.

(and if you didn't make any mistakes in calculation)

[hard loom]

I did this

Hanging on

[sturdy ember]

how does that show "a" is integer

[limber turtle]

Going back to your first question.

You have put k+1 as the formula of an odd integer.

What if k is 1?

That gives you 2.

Which is even.

2k+1 fits better assuming that k is an integer.

[sturdy ember]

(man I remember I proved this before and showed it to another person 💀 )

[hard loom]

I see

Does that change much in my current proof?

Besides adding the 2

[limber turtle]

i will work it out

on a piece of paper

give me a sec

[hard loom]

Ight

[limber turtle]

i think you need to prove by exhaustion

"every odd integer equal to the difference of two squares"

[hard loom]

But there's a non finite amount of options in the domain

[limber turtle]

you need to consider different circumstances

split the calculation into different cases

or perhaps assume that there is an even integer equal to the difference of two squares

that would be contradiction

[hard loom]

That's a indirect proof tho

[limber turtle]

let me have a look

you could do

2k+1 = (a-b)(a+b) and then

try different situations where a = 2k+1 and b = 2k+1 or a = 2k and b = 2k+1

[hard loom]

Is this still solving by contradiction?

[limber turtle]

no

that is exhaustion

[hard loom]

Oh sorry

So when working out the first case does that ones line end at 2k+1 = a^2 - b^2 or does it end at 2k+1 + b^2 = a^2

[sturdy ember]

honestly contradiction is easier, I recall that's the way I did

[hard loom]

I was gonna do it today way but the instructions say not to

[sturdy ember]

uh so I got ((a+b)(a-b)-1)/2=k

[hard loom]

Oh it's being used to find the value of k

[sturdy ember]

so just try proving (a+b)(a-b) can result to all odd numbers

my brain is having monday sickness

[hard loom]

I feel that, to bad I can't walk to a time zone that is in the future

[sturdy ember]

monday left me broken~

[hard loom]

Mhm Monday destroyer of energy, bane of the living

[hard loom]

How's that

[hard loom]

!close

[brisk cloak]

think you meant .solved

[hard loom]

Thanks

.solved