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26 December, 00:44

Prove that (n+5) ^2 - (n+3) ^2 is a multiple of 4 for all positive integer values of n.

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  1. 26 December, 02:51
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    (n+5) ² - (n+3) ² =

    = (n² + 10n + 25) - (n² + 6n + 9)

    = n² + 10n + 25 - n² - 6n - 9

    = 4n + 16

    = 4 (n + 4) ⋮ 4
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