(NCERT)
4. Show that any positive odd integer is of the form 6q +1,6q+ 3 or 6q+5, where q is some
integer.​

Question

(NCERT)
4. Show that any positive odd integer is of the form 6q +1,6q+ 3 or 6q+5, where q is some
integer.​

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Josie 2 months 2021-08-03T13:16:02+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-03T13:17:15+00:00

    Answer:

    According to Euclid’s division lemma

    a = bq + r

    a = 6q + r………………….(1)

    where, (0 ≤ r < 6)

    So r can be either 0, 1, 2, 3, 4 and 5.

    Case 1:

    If r = 1, then equation (1) becomes

    a = 6q + 1

    The Above equation will be always as an odd integer.

    Case 2:

    If r = 3, then equation (1) becomes

    a = 6q + 3

    The Above equation will be always as an odd integer.

    Case 3:

    If r = 5, then equation (1) becomes

    a = 6q + 5

    The above equation will be always as an odd integer.

    ∴ Any odd integer is of the form 6q + 1 or 6q + 3 or 6q + 5.

    Hence proved.

    Step-by-step explanation:

    0
    2021-08-03T13:17:46+00:00

    Step-by-step explanation:

    We know that,

    a = bq+r. {by Euclid’s division lemma}

    let the first integer be 6q,

    second be 6q+1

    third be 6q+2

    fourth be 6q+3

    fifth be 6q+4

    sixth be 6q+5

    From above we can see that second, fourth, and sixth are odd positive integers and can be written in the form 6q +1,6q+ 3 or 6q+5, while first, third,fifth cannot.

    Hence proved.

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