Question

Prove that only one of the no. n-1,n+1 or n+3 divisible by 3,where n is any positive integers

Answer 1

If n is divisible by 3 then n+3 is divisible by 3.If when 3 divided by n gives remainder 1,then n-1 is divisible by 3. If when 3 is divided by n gives remainder 2, then n+1 is divisible by 3. Thus n-1, n+1 or n+3 must be divisible by 3