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Math Help - Quadratic

  1. #1
    Junior Member Singular's Avatar
    Joined
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    Solo, Java
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    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 $n \in \mathbb{Z}^{+}$

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

    isn't quadratic number
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    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) .= .4n,
    . . which is a multiple of 4.

    If it is odd, its square is: .(2n + 1) .= .4n + 4n + 1 .= .4(n + 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.

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