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$$\:\:\:\:\:\:{show}\:{that}\: \\ $$$$\mathrm{8}^{{n}} \:−\mathrm{3}^{{n}} \:{is}\:{divisible}\:{by}\:\mathrm{5}\:\:{for}\:{all}\:{natural} \\ $$$${number}. \\ $$
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$$\: \\ $$$$\:\:\:\mathrm{4}^{{x}} +\mathrm{2}{x}^{\mathrm{2}} ={e}^{\mathrm{4}} \\ $$$$\:{Find}\:{x} \\ $$
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$${p}\left({t}\right)=\mathrm{4}{t}^{\mathrm{4}} +\mathrm{5}{t}^{\mathrm{3}} −{t}^{\mathrm{2}} +\mathrm{6}\:\:{at}\:\:{t}={a} \\ $$
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$$\boldsymbol{\mathrm{F}}\:=\:\frac{\boldsymbol{\mathrm{Gm}}_{\mathrm{1}} \boldsymbol{\mathrm{m}}_{\mathrm{2}} }{\boldsymbol{\mathrm{r}}^{\mathrm{2}} } \\ $$$$\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{r}}\:\:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}\: \\ $$$$\boldsymbol{\mathrm{equation}}. \\ $$
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