Given that the function f(x) has a domain of R and for any x,y∈R , the equation f(x−y)⋅f(x+y)=(f(x)−f(y))⋅(f(x)+f(y)) always holds true. Moreover, it is given that f(1)=2 and f(2)=0 . We are asked to find the value of f(2023)+f(2024) .
I tried this method and did not succeed in finding it.
RecurrenceTable[{f[x - y] f[x + y] == (f[x] - f[y]) (f[x] + f[y]),
f[1] == 2, f[2] == 0}, f, {x, 2024}, {y, 2024}]
