Question Number 162522 by HongKing last updated on 30/Dec/21
$$\mathrm{Determine}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integers} \\ $$$$\boldsymbol{\mathrm{N}}\:\mathrm{which}\:\mathrm{the}\:\mathrm{sphere} \\ $$$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} \:=\:\mathrm{N} \\ $$$$\mathrm{has}\:\mathrm{an}\:\mathrm{inseribed}\:\mathrm{regular}\:\mathrm{tetrahedron} \\ $$$$\mathrm{whose}\:\mathrm{vertices}\:\mathrm{have}\:\mathrm{integer}\:\mathrm{coordinates} \\ $$
Answered by mr W last updated on 30/Dec/21
Commented by HongKing last updated on 30/Dec/21
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{my}\:\mathrm{dear}\:\mathrm{Sir},\:\mathrm{solution}\:\mathrm{please} \\ $$