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8 April, 22:35

Prove that given any three consecutive integers, one of them is divisible by 3. Hint: What are the possible remainders when we divide an integer by 3?

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  1. 8 April, 22:59
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    it is proved that from the any three consecutive integers one of them is divisible by 3.

    Step-by-step explanation:

    Let the first integer = x

    The second consecutive integer = x + 1

    The third consecutive integer = x + 2

    Case 1. take x = 1

    The value of first integer = 1

    The value of second integer = 1 + 1 = 2

    The value of third integer = 1 + 2 = 3

    Here the third integer is divisible by 3.

    Case 2. take x = 2

    The value of first integer = 2

    The value of second integer = 2 + 1 = 3

    The value of third integer = 2 + 2 = 4

    Here the second integer is divisible by 3.

    Case 3. take x = 3

    The value of first integer = 3

    The value of second integer = 3 + 1 = 4

    The value of third integer = 3 + 2 = 5

    Here the first integer is divisible by 3.

    Thus it is proved that from the any three consecutive integers one of them is divisible by 3.
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