I only want the roots of the function to equal whole squares. So the function $\sin(\pi\times x)$ would not work, the roots can only be whole square numbers.
Can a periodic function be represented with roots $= x^2$ where $x$ is an element of the integers?
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periodic-functions
1 Answers
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$$f(x) = \cases{\sin(\pi\sqrt{x}),& $x\ge 0$\cr x, & $x < 0$}$$ $$f(x) = 0\iff x\ge0, \sin(\pi\sqrt{x}) = 0\iff x\ge0,\pi\sqrt{x} = k\pi, k\in\Bbb Z\iff x = k^2, k\in\Bbb Z.$$ But the condition of periodicity is impossible.
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0Can you explain this, I just need to have a function who's roots are only whole numbers squared, I need it as a tool for something, then I've solved the problem. – 2017-01-08
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0@Jack, see the edit. – 2017-01-08