Question Number 223735 by Nicholas666 last updated on 03/Aug/25
$$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{all}}\:\:{n}\:\in\:\mathbb{Z}\:, \\ $$$$\:\:\:\:\:\boldsymbol{\mathrm{Show}}\:\boldsymbol{\mathrm{that}}\:\tau\:\left(\:\varphi\:\left(\:{n}\:\right)\right)\:\geqslant\:\varphi\:\left(\tau\:\left({n}\:\right)\right) \\ $$$$ \\ $$