how would I prove this? (n^2 =/= 3t+2)

[stiff solar]

I've been stuck thinking about this one for a bit, I can't even figure out where I would begin.

My thinking started that I should figure out the relationship of a 'threven' number and squares, then work from there, but that doesn't seem to be helping.

Because the definition of threven, throdder, & throdder is essentially defining n%3, I thought maybe modulo would help but that hasn't been in this course so far, so I'm not certain.

Any hints on how to start this would be great, I want to figure it out so I can get stuck on the next one :p

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[stiff solar]

how would I prove this? (n^2 =/= 3t+2)

[magic trail]

Do you know Fermat’s little theorem ?

[stiff solar]

no, but i'll look it up now

[magic trail]

It’s not necessarily needed here, you can also do a proof without it

[stiff solar]

a^p = a%p
in this instance, since we're squaring n, it's n^2 = n%2, im not sure how that actually helps here

[magic trail]

Here p=3

n^2 can either be 0 or 1 mod (3) (why?)

[stiff solar]

i don't follow, the formula say n^p = n%p, so for n^2, p=2

i don't see how to turn that into p=3, without cubing n

[magic trail]

The theorem states that if p does not divide a then a^(p-1)=1 mod(p) consequently a^p=a mod(p) for any a

You can also work by cases if n=0,1 or 2 mod(3) then n^2 can’t be equal to 2 mod (3)

[magic trail]

(Try this approach)

If you don’t know the theorem that means you aren’t supposed to use it

[stiff solar]

sorry, im not following the fermat idea, the other one seems more likely to be the intended solution

[magic trail]

That’s fine, like you said you aren’t supposed to use it, use the other approach

[stiff solar]

wait, is this far easier than i was making it into? or have i done something wrong

the idea is i can extract 3 from as many terms as possible to show that for a term T, T%3=0, then ignore it, and show the rest never works

[magic trail]

Seems correct

[stiff solar]

i was caught up in showing how you would prove the relationship to n^2 but i guess i didn't need to, i just have to show how (3t+m)^2 works,
although looking back that is also, by given definition, the relationship to n^2

thanks mate

[magic trail]

Np

[stiff solar]

+close

[thick nimbus]

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