Prove that own and only one out of any three consecutive positive integers is divisible by 3.
Answers
Let the three consecutive positive integers be n,n+1,n+2
We know that n is of the form 3q,3q+1 or, 3q+2
Hence we can consider the following three cases:
Case I When n=3q n is divisible by 3 but it is not possible for n+1 and n+2
Case II When n=3q+1 n+2=3q+1+2=3 is divisible by 3 but it is not possible for n and n+1
Case III When n=3q+2 n+1=3q+1+2=3(q+1) is divisible by 3 but it is not possible for n and n+2
Hence one amongst n,n+1, and n+2 is divisible by 3.
SOLUTION :)
Let the three consecutive positive integers be n,n+1,n+2
We know that n is of the form 3q,3q+1 or, 3q+2
Hence we can consider the following three cases:
Case I When n=3q n is divisible by 3 but it is not possible for n+1 and n+2
Case II When n=3q+1 n+2=3q+1+2=3 is divisible by 3 but it is not possible for n and n+1
Case III When n=3q+2 n+1=3q+1+2=3(q+1) is divisible by 3 but it is not possible for n and n+2
Hence one amongst n,n+1, and n+2 is divisible by 3.