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Harmonic Functional Periodicity Quest (Posted on 2025-05-05)

Give a function f: R -> R such that f(x+1) + f(x-1) = f(x) * √3 for all x ∈ R. Prove that f is periodic and find its periodicity.

No Solution Yet Submitted by Danish Ahmed Khan

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Counter example?

Comment 1 of 1

Let f(x)=0 for all x, then for any real number, n,

f(n)=(f(n+1)+f(n-1))/sqrt(3)=(0+0)/sqrt(3)=0 which is consistent with the assumption.

This example is obviously not periodic. Maybe there is more to this than I am seeing?

Edited on May 9, 2025, 8:20 am

Posted by Kenny M on 2025-05-08 14:27:53

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