Find-all-real-a-such-that-f-x-ax-sinx-is-periodic-u-is-the-fractional-part-function-of-the-real-number-u-

Question Number 4748 by Yozzii last updated on 04/Mar/16

$${Find}\:{all}\:{real}\:\boldsymbol{{a}}\:{such}\:{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{f}\left({x}\right)=\left\{\boldsymbol{{a}}{x}+{sinx}\right\}\: \\ $$$${is}\:{periodic}.\:\left\{{u}\right\}\:{is}\:{the}\:{fractional}−{part} \\ $$$${function}\:{of}\:{the}\:{real}\:{number}\:{u}. \\ $$

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