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Show that the square of any …

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Show that the square of any odd positive integer is of the form 8m+1 for some integer m.

    • Posted by Vaishnavi Rajkumar 6 years, 6 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 6 months ago

    Since, any odd positive integer n is of the form 4m + 1 or 4m + 3.

    if n = 4m + 1
    n2 = (4m + 1)2
    = 16m2 + 8m + 1
    = 8(2m2 + m) + 1
    So n2 = 8q + 1 ........... (i)) (where q = 2m2 + m is a positive integer)

    If n = (4m + 3)
    n2 = (4m + 3)2
    = 16m2 + 24m + 9
    = 8(2m2 + 3m + 1) + 1
    So n2 = 8q + 1 ...... (ii) (where q = 2m2 + 3m + 1 is a positive integer)

    From (i) and (ii) we conclude that the square of an odd positive integer is of the form 8q + 1, for some integer q.

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