Question Number 193484 by Frix last updated on 15/Jun/23
![Nice problem: Find 8 distinctive numbers ∈N\{0} such that these are simultaniously true: (1) a+b+c+d = e+f+g+h (2) a^2 +b^2 +c^2 +d^2 = e^2 +f^2 +g^2 +h^2 (3) a^3 +b^3 +c^3 +d^3 = e^3 +f^3 +g^3 +h^3 [Find a method to generate such numbers]](https://www.tinkutara.com/question/Q193484.png)
$$\mathrm{Nice}\:\mathrm{problem}: \\ $$$$\mathrm{Find}\:\mathrm{8}\:\mathrm{distinctive}\:\mathrm{numbers}\:\in\mathbb{N}\backslash\left\{\mathrm{0}\right\}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{these}\:\mathrm{are}\:\mathrm{simultaniously}\:\mathrm{true}: \\ $$$$\left(\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\:\:\:{a}+{b}+{c}+{d}\:=\:{e}+{f}+{g}+{h} \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +{d}^{\mathrm{2}} \:=\:{e}^{\mathrm{2}} +{f}^{\mathrm{2}} +{g}^{\mathrm{2}} +{h}^{\mathrm{2}} \\ $$$$\left(\mathrm{3}\right)\:\:\:\:\:{a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} +{d}^{\mathrm{3}} \:=\:{e}^{\mathrm{3}} +{f}^{\mathrm{3}} +{g}^{\mathrm{3}} +{h}^{\mathrm{3}} \\ $$$$\left[\mathrm{Find}\:\mathrm{a}\:\mathrm{method}\:\mathrm{to}\:\mathrm{generate}\:\mathrm{such}\:\mathrm{numbers}\right] \\ $$