Question

Prove that every perfect square is \(0\) or \(1\) modulo 4.

Answer 1

Is this another even/odd proof?

Answer 2

by ft of a all exponents of prime factorization are even, so if it contains a 2 it contains a 4
now the question is, suppose it is odd, then what?

Answer 3

yes

Answer 4

Hmm...\[p^2 = (2n + 1)^2 = 4n^2 + 4n + 1\]

Answer 5

when even remainder is 0 and when odd remainder is 1

Answer 6

every no.is always of the form 4n ,4n+1,4n+2 or 4n+3

sq each,
you shhould get what you seek..

Answer 7

What now?

Answer 8

@shubhamsrg as the method if \(n^2\) is odd

Answer 9

**"has the method"

Answer 10

Ohh!

Answer 11

It's already in front of me.

Answer 12

mod 4 4(n)+1 is 1

Answer 13

Yes :)

Answer 14

Thanks all

Answer 15

@satellite73: My MSE username is Dumb Cow in case you wonder... :P