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So that the square of any …

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So that the square of any positive integers is of the form 3m,3m+1 for some integers m

    • Posted by Raja Jain 6 years, 5 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 5 months ago

    Let a be any positive integer and b = 3.
    Then a = 3q + r for some integer q ≥ 0
    And r = 0, 1, 2 because 0 ≤ r < 3
    Therefore, a = 3q or 3q + 1 or 3q + 2
    Or,
    a2 = (3q)2 or (3q + 1)2 or (3q + 2)2
    a2=9q2 or 9q2  +6q + 1 or 9q2 + 12q + 4
    =3 ​×​ (3q2) or 3(3q2+2q) +1 or 3(3q2+4q)+1
    =3k1 or 3k2+1 or 3k3+1
    Where k1 , k2 , and k3 are some positive integers

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