lean_workbook_plus_19806

Second, for powers 9, you could say : \n $y = 0\pmod{19}$ implies $y^9 = 0\pmod{19}$ \n $y\neq 0\pmod{19}$ implies $y^{18} = 1\pmod{19}$ (Fermat) \nBut the only squares equal to 1 $\pmod{19}$ are 1 and 18 (see above) \nAnd so $y^9$ can only be $0,1, 18$ $\pmod{19}$ .