If I, n are positive integers , `0 lt f lt 1` and if `(7 + 4sqrt3)^n = I +f`, then show that I is an odd integer

If I, n are positive integers , 0 lt f lt 1 and if (7 + 4sqrt3)^n = I +f , then show that (I+f) (1 - f) = 1

If R, n are positive integers, n is odd, 0lt F lt1" and if "(5sqrt(5)+11)^(n)=R+F, then prove that R is an even integer and

If (2+sqrt(3))^n=I+f, where I and n are positive integers and 0lt f lt1 , show that I is an odd integer and (1-f)(1+f) =1

If R, n are positive integers, n is odd, 0lt F lt1" and if " (5sqrt(5)+11)^(n)=R+F, then prove that (R+F).F=4^(n)

If (9 + 4 sqrt(5))^(n) = I + f , n and I being positive integers and f is a proper fraction, show that (I-1 ) f + f^(2) is an even integer.

If n in N such that (7 + 4 sqrt(3))^(n) = I + F , then IF is

If n is a positive integer, then ((n+4)!)/((n+7)!)=

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

For a positive integer n , find the value of (1-i)^(n) (1 - 1/i)^(n)

For a positive integer n , find the value of ( 1-i)^n(1-1/i)^ndot