If `(2+sqrt(3))^n=I+f,` whare `I` and `n` are positive integers and `0

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 (2+sqrt(3))^n=I+f, where I and n are positive integers and 0

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

If (7+4sqrt3)^n=I+F where I and n are +ve integers and F is +ve proper fraction, then (I+F)(1-F)=

If (4+sqrt15)^n=I+F when I, n are positive integers, 0 lt F lt 1 then (I+F)(1-F)=