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Problem on functions

Let f:R+ --> R be defined as f(x)=x + (1/x) -$$\lfloor$$ x + (1/x) $$\rfloor$$. It is required to prove that there are infintely many rational numbers u so that

$$\bullet\, 0<u<1,$$

$$\bullet\, u,\,f(u),\, f(f(u)) \:are\: all\: distinct,\: and$$

$$\bullet\, f(f(u))= \,f(f(f(u)))$$

Note by Nishant Sharma
4 years, 3 months ago

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a nice problem you gave but sorry i could not solve it...hope anyone comes forward to confront this problem...:( · 4 years, 3 months ago