Functional equations, number of solutions

f(x+y) = f(x) + f(y) - xy - 1

f(x+y) = f(x) + f(y) - xy - 1

f(x+y) = f(x) + f(y) - xy - 1

f(x+y) = f(x) + f(y) - xy - 1, x and y are real numbers, and

f(1) = 1

f(1) = 1

f(1) = 1

f(1) = 1, then the number of solutions of

f(n) = n

f(n) = n

f(n) = n

f(n) = n, where n is a natural number is?

A. one
B. no solution
C. three
D. None of these