Question Number 44333 by Tawa1 last updated on 27/Sep/18
$$\mathrm{Can}\:\mathrm{positive}\:\mathrm{integers}\:\:\mathrm{a},\:\mathrm{b},\:\mathrm{c}\:\:\mathrm{be}\:\mathrm{found}\:\mathrm{such}\:\mathrm{that}\:\:\:\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{3}} \:=\:\mathrm{c}^{\mathrm{3}\:\:\:} ? \\ $$
Commented by MrW3 last updated on 28/Sep/18
$${nobody}\:{has}\:{found}\:{such}\:{integers}\:{a},{b},{c} \\ $$$${that}\:{a}^{{n}} +{b}^{{n}} ={c}^{{n}} \:{with}\:{n}\geqslant\mathrm{3},\:{on}\:{the}\:{other}\:{side} \\ $$$${nobody}\:{has}\:{proved}\:{that}\:{such}\:{integers} \\ $$$${don}'{t}\:{exist}\:\left({or}\:{it}\:{is}\:{proved}?\right). \\ $$
Commented by Tawa1 last updated on 27/Sep/18
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$