Question Number 100290 by Harasanemanabrandah last updated on 26/Jun/20
Commented by Rasheed.Sindhi last updated on 26/Jun/20
$$\:^{\bullet} {If}\:\:{n}\:{is}\:{multiple}\:{of}\:\mathrm{3}\:\:{then}\:\mathrm{3}^{{n}} +{n}^{\mathrm{3}} \: \\ $$$${is}\:{obviously}\:\:{composite}\:\left(\mathrm{3}\:\mid\:\mathrm{3}^{{n}} +{n}^{\mathrm{3}} \right) \\ $$$$\:^{\bullet} {If}\:{n}\:{is}\:{odd}\:{then}\:\mathrm{3}^{{n}} +{n}^{\mathrm{3}} \:{is}\:{composite} \\ $$$$\left(\:\mathrm{2}\:\mid\:\mathrm{3}^{{n}} +{n}^{\mathrm{3}} \right) \\ $$$${Hence}\:{for}\:{n}\in\left\{\mathrm{3},\mathrm{6},\mathrm{9},...\right\}\cup\left\{\mathrm{1},\mathrm{3},\mathrm{5},...\right\} \\ $$$${the}\:{given}\:{expression}\:{is}\:{composite}. \\ $$