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Andrax
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Homework Statement
f(x+2)=f(x-1)f(x+5)
prove that there exists n natural number in which f(x+n)=f(x) like cos+2pi
Homework Equations
anyway i was doing some kind of solution i was pretty onfident that I am going to get the solution i was trying to make for example f(x+6)=f(x+3)f(x+9) we know< that f(x)=f(x-3)f(x+3) so f(x+3)=f(x)/f(x+3) [ignoring that the functoin is from R->R] was hoping that f(x+9)/f(x+3)=f(x+k) then i'll find this k suppose that f(x+6)=f(k)f(x) then f(x) = f(x+6)/f(k) then ill try to find the k from the first equatoin this got me in troubles cause it iddn't work iwas surprised that i didn't work..
The Attempt at a Solution
it seems like the only way anyway final thing I've reached is simplifying
f(x+n)=f(x+n+3)f(x+n-3) n is a natural number
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