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 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 let then (D)/((n-1)!(n+1)!(n+3)!) is equal to

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 is an odd positive integer,show that (n^(2)-1) is divisible by 8.

For all n in N , 4^(n)-3n-1 is divisible by

If n is a positive integer,then show tha 3^(2n+1)+2^(n+2) is divisible by 7.

If n is a positive integer show that (n+1)^(2)+(n+2)^(2)+....4n^(2)=(n)/(6)(2n+1)(7n+1)

10^n+3(4^(n+2))+5 is divisible by (n in N)