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Show that any positive odd integer …

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Show that any positive odd integer is of the form q+1,6q+3,6q+5 where q is some integer (Hint:b= 6, r= 0,1,2,3,4,5,(0<r<6))

    • Posted by Aarti Trivedi 5 years, 4 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Gaurav Seth 5 years, 4 months ago

     

    For any two numbers a and b, there exists q and r such that

    a = bq + r  .... Using euclid division algorithm

    Here 0 <= r < b

    Taking b = 6, a = 6q + r

    where 0 <= r < 6

    This means r can take the values 0, 1, 2, 3, 4 and 5

    When r = 0, 2, 4 the value of a will be 6q, 6q+2, 6q+r which are even

    When r = 1, 3, 5

    a = 6q + 1, a = 6q + 3, a = 6q + 5 are all odd numbers.

    Hence, any positive odd integer is of the form 6q + 1, 6q + 3 or 6q + 5

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