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Show that nsqaur is divisible by …

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Show that nsqaur is divisible by 8 if n is odd positive integer

    • Posted by Yash Khatode 5 years, 3 months ago

    CBSE > Class 10 > Mathematics
    • 2 answers

    Jags Sma 5 years, 3 months ago

    Any odd positive integer n can be written in form of 4q + 1 or 4q + 3.   If n = 4q + 1, when n2 - 1 = (4q + 1)2 - 1 = 16q2 + 8q + 1 - 1 = 8q(2q + 1) which is divisible by 8. If n = 4q + 3, when n2 - 1 = (4q + 3)2 - 1 = 16q2 + 24q + 9 - 1 = 8(2q2 + 3q + 1) which is divisible by 8. Here is the answer Mark it as expert answer ;);)

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    Gaurav Seth 5 years, 3 months ago

    Show that n2 - 1 is divisible by 8, if n is an odd positive integer.

    Any odd positive integer n can be written in form of 4q + 1 or 4q + 3.

     

    If n = 4q + 1, when n2 - 1 = (4q + 1)2 - 1 = 16q2 + 8q + 1 - 1 = 8q(2q + 1) which is divisible by 8.

    If n = 4q + 3, when n2 - 1 = (4q + 3)2 - 1 = 16q2 + 24q + 9 - 1 = 8(2q2 + 3q + 1) which is divisible by 8.

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