Question

Prove that one of every three consecutive positive integer is divisible by 3

Answer 1

Let 3 consecutive positive integers be n, n+1 and n+2

Whenever a number is divided by 3, the remainder we get is either 0, or 1, or 2.
:
Therefore:


n = 3p or 3p+1 or 3p+2, where p is some integer

If n = 3p, then n is divisible by 3

If n = 3p+1, then n+2 = 3p+1+2 = 3p+3 = 3(p+1) is divisible by 3

If n = 3p+2, then n+1 = 3p+2+1 = 3p+3 = 3(p+1) is divisible by 3

Thus, we can state that one of the numbers among n, n+1 and n+2 is always divisible by3

Answer 2

Step-by-step explanation:

Let 3 consecutive positive integers be n, n + 1 and n + 2 .

Whenever a number is divided by 3, the remainder we get is either 0, or 1, or 2.

:

Therefore:

n = 3p or 3p+1 or 3p+2, where p is some integer

If n = 3p = 3(p) , then n is divisible by 3

If n = 3p + 1, then n + 2 = 3p +1 + 2 = 3 p + 3 = 3 ( p + 1 ) is divisible by 3

If n = 3p + 2, then n + 1 = 3p + 2 + 1 = 3p + 3 = 3(p + 1) is divisible by 3

Thus, we can state that one of the numbers among n, n+1 and n+2 is always divisible by 3

Hence it is solved.

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