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Math Help - Discrete!!!! Please Help

  1. #1
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    Discrete!!!! Please Help

    Prove that if n is a positve even integer, then n^2 = 0(mod 8) or n^2= 4(mod 8).
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  2. #2
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    Hello, jas05s!

    Prove that if n is a positve even integer, then: . n^2 \equiv 0\text{ (mod 8) }\text{ or }\;n^2 \equiv 4\text{ (mod 8)}

    Since n is an even integer, n \;=\;4k\text{ or }4k+2
    . . ( n is a multiple of 4, or two more than a multiple of 4.)

    If n = 4k\!:\;\;n^2\:=\:16k^2 \:=\:8(2k^2) \:\equiv\:0\text{ (mod 8)}

    If n \:=\:4k+2\!:\;\;n^2 \:=\:16k^2 + 16k + 4 \:=\:8(2k^2 + 2k) + 4 \:\equiv \:4\text{ (mod 8)}

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