х¹⁶ - у¹⁶ =(х+у)(х²+у²)(х⁴+у⁴)(х⁸+у⁸)
х-у
1) х¹⁶-у¹⁶=(х⁸-у⁸)(х⁸+у⁸)=(х⁴-у⁴)(х⁴+у⁴)(х⁸+у⁸)=(х²-у²)(х²+у²)(х⁴+у⁴)(х⁸+у⁸)=
=(х-у)(х+у)(х²+у²)(х⁴+у⁴)(х⁸+у⁸)
2) (х-у)(х+у)(х²+у²)(х⁴+у⁴)(х⁸+у⁸) = (х+у)(х²+у²)(х⁴+у⁴)(х⁸+у⁸)
х-у
(х+у)(х²+у²)(х⁴+у⁴)(х⁸+у⁸)=(х+у)(х²+у²)(х⁴+у⁴)(х⁸+у⁸)
Тождество доказано.