Number Theories

[true hill]

There should only be the solution (2, 3), but idk.

[crisp dust]

3?

No odd no would satisfy the above condition

[fading drift]

Give me a second

I believe I can solve this

[ancient halo]

hey randel any luck

[fading drift]

Yeah

Almost there

[ancient halo]

(2,3) does satisfy those conditions

[fading drift]

I can send a screenshot of the proof

But I believe giving hints is a better way of understanding the solution

@true hill , you there?

[ancient halo]

i doubt her the lady's presence randel

[fading drift]

Yeah

Okay

I can try and explain it to you ronald

Maybe she can check our chat later

Alright let's begin

[ancient halo]

sure go ahead

[tawdry stirrup]

Randel_

[ancient halo]

i have realized that if you line up the squares in order they add by 3,5,7 that's something

[fading drift]

Maybe, but it is not the direction I've taken with the solution

[tawdry stirrup]

Randel_

[fading drift]

Got it?

[ancient halo]

yeah i once recreated that so i can agree straight on!!

[fading drift]

Okay

But remember, p is a prime number

This is very important

Prime numbers have only 2 factors- 1 and the number itself

[ancient halo]

yeah has no factors got it wait but

aren't those already factors

[fading drift]

What

[fading drift]

Which ones

[ancient halo]

the n+1 and that other one

[fading drift]

Yeah

Exactly

So

This leads us to 3 situations

[ancient halo]

maybe if each equals p

then it'd be p times p p^2

[tawdry stirrup]

Randel_

Randel_

[ancient halo]

oh yeah that's possible

that too ofc

[tawdry stirrup]

Randel_

[fading drift]

As you've mentioned

[ancient halo]

yeah pal

[fading drift]

Now we solve for each one

[ancient halo]

wait but

[tawdry stirrup]

Randel_

[ancient halo]

is n+1 = p^2 and the other 1 p0ossible

isn't n+1 bound to be smaller

the smaller one

n^2-n+1 must be bigger in most cases right

[tawdry stirrup]

Randel_

[fading drift]

Yeah, I think so

But I don't think we need that

[tawdry stirrup]

Randel_

[ancient halo]

yeah for n=n^2-n only 2 can satisfy

and 0 maybe

but 0 isn't prime so no

3 =2+1 is prime so yes

[fading drift]

Here are my notes if anything is unclear

[ancient halo]

i agree i've given it a thought

[fading drift]

Do you understand everything?

[ancient halo]

but have we run through all possible scenarios for the 1st one

[fading drift]

Yes

[tawdry stirrup]

Randel_

[ancient halo]

oh it has to equal to 1 yeah no chance

[fading drift]

Yeah

Any other doubts

[ancient halo]

well if n+1 and n^2-n+1 have to be the same for the third scenario let me add

n has to = n^2-n

[fading drift]

Yeah

[ancient halo]

meaning that from n to n^2 you added n

and to add itself is to *by 2

[fading drift]

$n=n^2-n$, which leads us to $n^2 - 2n = 0$

[tawdry stirrup]

Randel_

[ancient halo]

so only 2 satisfies it

[fading drift]

Yes

And 0

[ancient halo]

but 1 isn't prime so

[fading drift]

Correct

[ancient halo]

WE HAVE SOLVED IT

mostly you of course

[fading drift]

dw

You did great, too

[ancient halo]

how old r u anyway

you are in pre so i was curious you know all this

ha yeah i just love math

and physics

[fading drift]

Same

[ancient halo]

i think we're done here

[fading drift]

Yeah

Hopefully it is helpful to Maryta

Anyways, see you on the server 👋

[ancient halo]

yeah bye

you can invite me to a question if u want to do it together 😉

[fading drift]

Seems right, but you need to reject these two situations first

[fading drift]

.

[fading drift]

.

No problem 🙂

Have a nice one 👋