Let A = {0, 1, 2, 3, 4, 5, 6, 7}. Then the number of bijective functions f : A $$\to$$ A such that f(1) + f(2) = 3 $$-$$ f(3) is equal to

If f(x) and g(x) are two polynomials such that the polynomial P(x) = f(x³) + x g(x³) is divisible by x² + x + 1, then P(1) is equal to ___________.

If a + $$\alpha$$ = 1, b + $$\beta$$ = 2 and $$af(x) + \alpha f\left( {{1 \over x}} \right) = bx + {\beta \over x},x \ne 0$$, then the value of the expression $${{f(x) + f\left( {{1 \over x}} \right)} \over {x + {1 \over x}}}$$ is __________.

Suppose that a function f : R $$ \to $$ R satisfies
f(x + y) = f(x)f(y) for all x, y $$ \in $$ R and f(1) = 3.
If $$\sum\limits_{i = 1}^n {f(i)} = 363$$ then n is equal to ________ .