證明所有平方數除4皆餘1or0

設偶數為2n，奇數為2n+1
(2n)^2, =4n^2
(2n+1)^2, =4n^2+1
∴証畢

錯。

低b仔

Freshman's dream

What?
He is correct?
My GOD!!!!
(x + y)^2 = x^2 + y^2 ???!!!
He is the best answer?!

The question should be stated clearly that:
The remainder is 1 or 0 when a square "integer " is divided by 4.


For even numbers 2n,
(2n)^2 = 4n^2
4n^2 is divisible by 4. The remainder is 0.


For odd numbers (2n + 1),
(2n + 1)^2 = 4n^2 + 4n + 1 = 4(n^2 + n) + 1
So the remainder is 1.



Combining the results, the remainder is 1 or 0 when an square integer is divided by 4.