Let $$f:R \to R$$ be a function such that $$f(x) = {{{x^2} + 2x + 1} \over {{x^2} + 1}}$$. Then

The number of functions

$$f:\{ 1,2,3,4\} \to \{ a \in Z|a| \le 8\} $$

satisfying $$f(n) + {1 \over n}f(n + 1) = 1,\forall n \in \{ 1,2,3\} $$ is

Let $$f:\mathbb{R}\to\mathbb{R}$$ be a function defined by $$f(x) = {\log _{\sqrt m }}\{ \sqrt 2 (\sin x - \cos x) + m - 2\} $$, for some $$m$$, such that the range of $$f$$ is [0, 2]. Then the value of $$m$$ is _________

Let $$f(x) = 2{x^n} + \lambda ,\lambda \in R,n \in N$$, and $$f(4) = 133,f(5) = 255$$. Then the sum of all the positive integer divisors of $$(f(3) - f(2))$$ is