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-

Question Number 193484 by Frix last updated on 15/Jun/23

Nice problem :

Find 8 distinctive numbers \in 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]