If n is a natural number, then 4n-3n-1 is  divisible by which one of the following?

Putting, n=2, we get 4n-3n-1=16-6-1=9 Putting, n=3 , we get 4n-3n-1=64-9-1=54 Putting, n=4, we get 4n-3n-1=256-12-1=243 Hence, for any value of n,4n-3n-1 is  always divisible by 9 .    second method:   1+3n-3n-1= 1+Cn,13+Cn,232+Cn,333+.....+3n-3n-1                              = 9Cn,2+Cn,33........ which is divisible by 9