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Show that any positive integer is …

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Show that any positive integer is of the form 3q, 3q+1, 3q+2, where q is some integer

    • Posted by Arpan Narain 4 years, 4 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Preeti Dabral 4 years, 4 months ago

    Let p be any positive integer and b = 3. Applying division Lemma with p and b =3 ,

    we have
    p = 3q + r, where 0 {tex}\leq{/tex} r < 3 and q is some integer

    So r=0,1,2

    If r=0 , p=3q

    If r=1, p=3q+1

    If r=2, p=3q+2

    Therefore any positive integer  is of form 3q,3q+1,3q+2 for some integer q.

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