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?

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.