2. Prove that one of every three consecutive positive integers is divisible by 3​

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2. Prove that one of every three consecutive positive integers is divisible by 3​

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Adalyn 7 months 2021-10-15T21:38:57+00:00 1 Answer 0 views 0

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    2021-10-15T21:40:14+00:00

    Answer:

    Let a, a+1, a+2 be the three consecutive positive integers.

    Then, a is of the 3q, 3q+1, 3q+2 .

    When a=3q

    therefore, a = 3q

    It is divisible by 3.

    when a =3q+1

    therefore, a+2 =3q+1 +2

    = 3q+3

    =3(q+1)

    =3k, k =q+1 is an integer.

    It is divisible by 3.

    when, a=3q+2

    therefore , a+1= 3q+2+1

    =3q+3

    =3(q+1)

    3k, k= q+1 is an integer.

    It is divisible by 3.

    Hence, one of the three consecutive positive integers is divisible by 3.

    Hope you like it.

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