Thread: Quadratic

Anyone know how to determine a number is quadratic (perfect square i don't know what it's called ) or note?

for example:

for $\displaystyle $n \in \mathbb{Z}^{+}$$

proof that $\displaystyle $(n-1)^{2}+(n-2)^{2}+n^{2}+(n+1)^{2}+(n+2)^{2}$$

isn't quadratic number

Hello, Singular!

There is a test for showing that an integer is not a square.

Theorem: The square of an integer must be either a multiple of 4
. . . . . . . .or one more than a multiple of 4.

Proof: an integer must be even (2n) or odd (2n + 1).

If it is even, its square is: .(2n)² .= .4n²,
. . which is a multiple of 4.

If it is odd, its square is: .(2n + 1)² .= .4n² + 4n + 1 .= .4(n² + n) + 1
. . which is one more than a multiple of 4.


In other words, a square must end in 0, 1, 4, 5, 6, or 9.