Solution:
Chinese
ORIGINAL VERSION
Chinese Translation of junk eggs, porn
Verify that:
FIB (0) was established, FIB (1) was established, FIB (2) was established, assuming fib (n) was established, then (the two Latin letters were replaced by x y ):
X = (1 + SQRT (5)/2, y = (1-sqrt (5)/2
FIB (n + 1) = fib (n) + fib (n-1) =... = (x + 1) * POW (x, n-1)-(Y + 1) * POW (Y, n-1)/SQRT (5)
Because x + 1 = POW (x, 2), Y + 1 = POW (Y, 2)
Therefore, FIB (n + 1) = (POW (x, n + 1)-Pow (Y, n + 1)/SQRT (5)
Therefore, FIB (n) = (POW (x, n)-Pow (Y, n)/SQRT (5) was established.
Prove that:
FIB (N)-Pow (x, N)/SQRT (5) = (POW (x, n)-Pow (Y, n)/SQRT (5) -Pow (x, N)/SQRT (5) =-Pow (Y, N)/SQRT (5)
When N is an odd number, FIB (n)> POW (x, N)/SQRT (5 ),
(POW (x, N)/SQRT (5)-(FIB (N)-1)-(FIB (N)-Pow (x, n) /SQRT (5)> 0
Similarly, when n is an even number, FIB (n) <POW (x, N)/SQRT (5 ),
(FIB (n) + 1)-Pow (x, N)/SQRT (5)-(POW (x, N)/SQRT (5) -fib (N)> 0
Therefore, FIB (n) is an integer closest to POW (x, N)/SQRT (5.