If n is an odd positve integer greater than 3 then `(n^3-n^2)-3(n^2-n)` is always a multiple of

If n is an odd number greater than 1, then n(n^(2)-1) is

Show that, if n be any positive integer greater than 1, then (2^(3n) - 7n - 1) is divisible by 49.

If n be a positive integer greater than 1, prove that (frac(n+1)(2))^n > n

If n is a positive integer and (n + 1)(n + 3) is odd, then (n + 2)(n + 4) must be a multiple of which one of the following?

If n is a positive integer (gt1) ,show that , 3^(2n+2)-8n-9 is always divisible by 64.

It is given that n is an odd integer greater than 3 but n is not a multiple of 3 prove that x^3+x^2+x is a factor of (x+1)^n-x^n-1:

If n is any odd number greater than 1, then n backslash(n^(2)-1) is divisible by 24 always (b) divisible by 48 always (c) divisible by 96 always (d) None of these

It is given that n is an odd integer greater than 3 but n is not multiple of 3. prove that (x^(3)+x^(2)+x) is a factor of (1+x)^(n)-x^(n)-1 .