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Show that any positive odd integer …

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Show that any positive odd integer is of the form 4q+ 3 where q is some whole number

    • Posted by Varun Kumar 6 years, 4 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 4 months ago

    By Euclid's division algorithm,
    a = bq + r = 4q + r
    Take b = 4.
    Since, 0 {tex}\leqslant{/tex} r < 4, r = 0,1, 2, 3
    {tex} a=4q,4q+1,4q+2 ,4q+3{/tex}
    Clearly, a =4q=2(2q) and 

    4q+2=2×(2q+1)

    So 4q and 4q+2 are even

    Therefore 4q + 1, 4q + 3 are odd, as they are proceeding numbers of even numbers 4q and 4q+2.
    {tex}\therefore{/tex} Any positive odd integer is of form 4q+1 or  4q+3 .Where q is a positive integer.

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