Question

prove that oneof any three consecutive positive integer must be divisible by 3...?? give me answer please.​

Answer 1

To prove:-

❥ One of any three consecutive positive integer must be divisible by 3.

Proof:-

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

❥ If a number is divided by 3, the remainder should be either 0 or 1 or 2.

∴ 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.

Hence, we can say that one of the numbers among n, n + 1 and n + 2 is always divisible by 3.

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Answer 2

Answer:-

To prove that:-

• One of every three consecutive positive integer is divisible by 3

Proof:-

Let n, n+1, n+2 be three consecutive positive integers

We know that:-

n is of the from of 2q, 3q+1, 3q+2

so, we have the following

Case 1:-

When n=3q

In this case, n is divisible by 3 but n+1 and n+2 are not divisible by 3

Case 2:-

When n = 3q+1

In this case, n+2 = 3q + 1 + 2 = 3 is divisible by 3 but n and n+1 are not divisible by 3

Case 3:-

When n = 3q + 2

In this case, n+1 = 3q + 1 + 2 = 3 ( a + 1 ) is divisible by 3 but n and n + 2 are not divisible by 3

Therefore, one of n, n+1, n+2 is divisible by 3