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Question Number 209309 by hardmath last updated on 06/Jul/24

$$\mathrm{m},\mathrm{n}\in \mathbb{N}$$$$\mathrm{m}⩾2\mathrm{and}\mathrm{n}⩾2$$$$\mathrm{p}>0\mathrm{and}\mathrm{q}>0$$$$\mathrm{p}+\mathrm{q}=1$$$$\mathrm{Prove}\mathrm{that}:{(1-{\mathrm{q}}^{\mathbf{n}})}^{\mathbf{m}}+{(1-{\mathrm{p}}^{\mathbf{m}})}^{\mathbf{n}}⩾1$$

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