1) 721+4921+34321+240121=
721+(7⋅7)21+(7⋅7⋅7)21+(7⋅7⋅7⋅7)21=
721+(721)2+(721)3+(721)4;
2) 721=7⋅(720)=7⋅(720+1)−7
3) Rem[721/(720+1)]=−7
We have represented 721 as 7⋅(720+1)−7 (look step 2)
7⋅(720+1)−7 mod (720+1) = -7 because
721+17⋅(721+1)−7=721+17⋅(721+1)+721+1−7=7+721+1−7
where is -7 is our reminder.
For steps 4, 5, 6 We have to raise our reminder to a power.
4) Rem[(721)2/(720+1)]=(−7)2
5) Rem[(721)3/(720+1)]=(−7)3
6) Rem[(721)4/(720+1)]=(−7)4
Answer:−7+(−7)2+(−7)3+(−7)4=2100
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