Question Number 32610 by naka3546 last updated on 29/Mar/18
$$\mathrm{2}.\:\:{Find}\:\:{the}\:\:{number}\:\:{of}\:\:{ordered}\:\:{triples}\:\:\left({a},\:{b},\:{c}\right)\:\:{of}\:\:{integers}\:\:{satisfying}\:\:\:\:\mathrm{0}\:\leqslant\:\:{a},\:{b},\:{c}\:\:\leqslant\:\:\mathrm{1000}\:\:\:{for}\:\:{which} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}^{\mathrm{3}} \:+\:{b}^{\mathrm{3}} \:+\:{c}^{\mathrm{3}} \:\:\equiv\:\:\mathrm{3}{abc}\:+\:\mathrm{1}\:\:\:\left({mod}\:\:\mathrm{1001}\right)\: \\ $$
Commented by Rasheed.Sindhi last updated on 30/Mar/18
$$\left(\mathrm{1},\mathrm{0},\mathrm{0}\right),\left(\mathrm{0},\mathrm{1},\mathrm{0}\right)\:\&\:\left(\mathrm{0},\mathrm{0},\mathrm{1}\right)\:\mathrm{are}\:\mathrm{satisfying} \\ $$$$\:\:\:\left(\mathrm{Not}\:\mathrm{complete}.\right)\:\: \\ $$$$ \\ $$