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If a , b are two fixed positive integers...

If `a , b` are two fixed positive integers such that `f(a+x)=b+[b^3+1-3b^2f(x)+3b{f(x)}^2-{f(x)}^3]^(1/3)` for all real `x ,` then prove that `f(x)` is periodic and find its period.

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