It is known that f (x) is an odd function and satisfies f (x + 1) = (1 + F (x)) / (1-f (x)). It is proved that 4 is a period of F (x)

It is known that f (x) is an odd function and satisfies f (x + 1) = (1 + F (x)) / (1-f (x)). It is proved that 4 is a period of F (x)

Syndrome: F (x + 2) = [1 + F (x + 1)] / [1-f (x + 1)]
F (x + 1) = (1 + F (x)) / (1-f (x)) is simplified
f(x+2)=-1/f(x)
So f (x + 4) = - 1 / F (x + 2) = f (x)
So 4 is a period of F (x)