Question Number 144421 by loveineq last updated on 25/Jun/21
$$\mathrm{Let}\:{a},{b},{c}\:>\:\mathrm{0}\:\mathrm{and}\:{a}+{b}+{c}\:=\:\mathrm{3}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{\mathrm{2021}} +{b}^{\mathrm{2021}} +{c}^{\mathrm{2021}} }{\mathrm{3}}\:\geqslant\:\mathrm{1}+\frac{\mathrm{4042}}{\mathrm{3}}\left(\mathrm{1}−\frac{{ab}+{bc}+{ca}}{\mathrm{3}}\right)\:\:\:\:\:\:\:\:\:\:\: \\ $$