A function f (x) defined on a positive integer set has f (M + n) = f (m) + F (n) + 4 (M + n) - 2 for any m, n ∈ n *, and f (1) = 1 (1) Find the expression of function f (x); (2) If m ^ 2-tm-1 ≤ f (x) belongs to [- 1,1] for any m and X belongs to n * constant, the value range of real number T is obtained; (3) For any positive integer n, there are always m + 1 real numbers A1, A2,... In [2, N + 16 / N] , am, am + 1, so that f (A1) + F (A2) + +f(am)

A function f (x) defined on a positive integer set has f (M + n) = f (m) + F (n) + 4 (M + n) - 2 for any m, n ∈ n *, and f (1) = 1 (1) Find the expression of function f (x); (2) If m ^ 2-tm-1 ≤ f (x) belongs to [- 1,1] for any m and X belongs to n * constant, the value range of real number T is obtained; (3) For any positive integer n, there are always m + 1 real numbers A1, A2,... In [2, N + 16 / N] , am, am + 1, so that f (A1) + F (A2) + +f(am)

(1) From F (M + n) = f (m) + F (n) + 4 (M + n) - 2
Then f (n)
=f(n-1+1)
=f(n-1)+f(1)+4n-2
=f(n-1)+4n-1
=f(n-2)+4(n-1)-1+4n-1
=f(1)+4*1+4*2+…… +4(n-1)+4n-(n-1)
=1+4n(n-1)/2-n+12n^2-3n+2
=2n^2-3n+2
Then f (x) = 2x ^ 2-3x + 2, (x ∈ n +)
(2) Let g (m) = m ^ 2-tm-1, then only G (m) max is needed