Show that if n is an integer greater then 1 , then n does not divide `2^n-1` .

If n is an odd integer greater than or equal to 1, then the value of n^3 - (n-1)^3 + (n-1)^3 - (n-1)^3 + .... + (-1)^(n-1) 1^3

If n is ann integer greater than 1, then a-^(n)C_(1)(a-1)+.^(n)C_(2)(a-2)- . . .+(-1)^(n)(a-n)=

Prove that x^3 + x^2 + x is factor of (x+1)^n - x^n -1 where n is odd integer greater than 3, but not a multiple of 3.

If n is a positive integer then 2^(4n) - 15n - 1 is divisible by

If n is n odd integer that is greater than or equal to 3 but not a multiple of 3, then prove that (x+1)^n-x^n-1 is divisible by x^3+x^2+xdot

If n is n odd integer that is greater than or equal to 3 but not a multiple of 3, then prove that (x+1)^n-x^n-1 is divisible by x^3+x^2+xdot

Prove that int_0^oo[n e^(-x)]dx=1n((n^n)/(n !)),w h e r en is a natural number greater than 1 and [.] denotes the greatest integer function..

When the integer n is divided by 2, the quotient is u and the remainder is 1. When the integer n is divided by 5, the quotient is v and the remainder is 3. Which one of the following must be true?

If n is a positive integer greater than unity z is a complex number satisfying the equation z^n=(z+1)^n, then

If n is any positive integer, write the value of (i^(4n+1)-i^(4n-1))/2 .