need a small help in understanding the solution

[craggy burrow]

" then taking
modulo 4 we see the 2n + 12n + 2011n ≡ 3 (mod 4), so it is not a square "

what does this line mean?

[severe junco]

0^2 = 0 modulo 4
1^2 = 1 modulo 4
2^2 = 0 modulo 4
3^2 = 9 = 1 modulo 4

There is no square that is equal to 3 modulo 4

[craggy burrow]

how is modulo 4 expressed?

[severe junco]

If you dont understand the word modulo

Then thats another issue

[craggy burrow]

how is it expressed in handwriting?

[severe junco]

Three bars ?

For example

If you take a number N

And perform euclidean division of N by 4

You can write N = 4q + r

With (q;r) being the quotient and remainder

[craggy burrow]

okok

understood

TYSM

[severe junco]

We say N = r modulo 4

Because the rest of the division of N by 4 is r

[craggy burrow]

unaware of the term 😅

[severe junco]

It's standard

[craggy burrow]

.close

[thin marlin]

Solved

Post marked as solved by @craggy burrow.

Use .unsolved if this was a mistake.

[severe junco]

".close" is the equivalent of " ok bye"

[craggy burrow]

ok bye