Question

Prove that only one of the numbers n-1, n+1 or n+3 is divisible by 3, where n is any positive integer. Explain.

Answer 1

Answer:

Step-by-step explanation:

Prove that only one of the numbers n-1, n+1 or n+3 is divisible by 3, where n is any positive integer. Explain.

n can be any one of these = 3k , 3k+1 or 3k+2  where k is integer

Let say n = 3k

then

n - 1 = 3k -1

n + 1 = 3k +1

n + 3 = 3k +3 = 3(k + 1)  ( divisible by 3)

Let say n = 3k+1

then

n - 1 = 3k + 1 -1 = 3k   ( divisible by 3)

n + 1 = 3k +1 +1 = 3k + 2

n + 3 = 3k + 1 +3 = 3(k + 1) + 1

Let say n = 3k+2

then

n - 1 = 3k + 2 -1 = 3k  + 1

n + 1 = 3k +2+1 = 3(k + 1)   ( divisible by 3)

n + 3 = 3k + 2 +3 = 3(k + 1) + 2

Only one number is divisible by 3