Let f (x) be a function defined on the real number set R and satisfy f (x + 2) = f (x + 1) - f (x). If f (1) = Lg3 / 2, f (2) = LG15, find f (2001) | Math enthusiast | Mathematical art

Let f (x) be a function defined on the real number set R and satisfy f (x + 2) = f (x + 1) - f (x). If f (1) = Lg3 / 2, f (2) = LG15, find f (2001)

Because f (x + 2) = f (x + 1) - f (x) f (x + 3) = f (x + 2) - f (x + 1) = f (x + 1) - f (x) - f (x + 1) = - f (x) f (x + 6) = - f (x + 3) = f (x), f (x) is a function with period 6, because f (2001) = f (6 * 333 + 3) = f (3) because f (3) = f (2) - f (1) = lg15-lg3 / 2 = LG10 = 1

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