show that any postive odd positive interger is of the form bq+1 or bq+3 or bq+5 where q is same interger​

Question

show that any postive odd positive interger is of the form bq+1 or bq+3 or bq+5 where q is same interger​

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Faith 3 weeks 2021-11-07T09:08:57+00:00 2 Answers 0 views 0

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    0
    2021-11-07T09:10:22+00:00

    Any number divided, can be written in the form of  \boxed{\sf{a = bq + r}}

    Where,

    • a = divident
    • b = divisor
    • q = quotient
    • r = remainder

    a = bq + r ” where r = 0, 1, 2, 3, 4, 5.

    But in the question it is mentioned positive odd integers, so r = 1, 3, 5.

    \sf{\red{When\:r=1}},

    ⟹ a = bq + 1

    \sf{\green{When\:r=3}},

    ⟹ a= bq + 3

    \sf{\blue{When\:r=5}},

    ⟹ a = bq + 5.

    ______________________

    \sf{Hence\:Proved!}

    0
    2021-11-07T09:10:32+00:00

    Answer:

    Any odd integer is of the form bq+1 or bq +3 or bq +5.

    Step-by-step explanation:

    Let us start with taking a ,where a is a positive integer. We apply the division algorithm with a and b.

    Since 0< r<b ,the possible reminder are 0,1,2,and 3.

    That is ,a can be bq+1 or bq+3 or bq+5,where q is the quotient.

    However ,since a is odd a can be bq+1 or bq+2 or bq+5.

    Therefore any odd integer is of the form bq+1 or bq+3 or bq+5.

    Hope it helps you.

    please mark as brain list.

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