For a fixed positive integer `n ,` if `=|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)!(n+2)!(n+3)!(n+4)!|` , then show that `[/((n !)^3)-4]` is divisible by `ndot`

For a fixed positive integer n , if Delta=|[n !,(n+1)!,(n+2)!],[(n+1)!,(n+2)!,(n+3)!],[(n+2)!,(n+3)!,(n+4)!]| , then show that [Delta/((n !)^3)-4] is divisible by ndot

For a fixed positive integer n if D= |(n!, (n+1)!, (n+2)!),((n+1)!, (n+2)!, (n+3)!),((n+2)!, (n+3)!, (n+4)!)| = the show that D/((n!)^3)-4 is divisible by n.

For a fixed positive integer n prove that: D = |[n!, (n+1)!, (n+2)!],[(n+1)!,(n+2)!,(n+3)!],[(n+2)!,(n+3)!,(n+4)!]|= ( n !)^3(2n^3+8n^2+10n+4 )

If n is a positive integer,show that 4^(n)-3n-1 is divisible by 9

If n is a positive integer, show that 4^n -3n -1 is divisible by 9

If n (> 1)is a positive integer, then show that 2^(2n)- 3n - 1 is divisible by 9.

If n is a positive integer, show that: 4^n-3n-1 is divisible by 9

If n is a positive integer, show that: 4^n-3n-1 is divisible by 9