Question 94
Find the number of functions $f$ from the set $S=\{0,1,2,\ldots,2020\}$ to itself such that, for all $a,b,c\in S$, all three of the following conditions are satisfied:
- (i) If $f(a)=a$, then $a=0$.
- (ii) If $f(a)=f(b)$, then $a=b$.
- (iii) If $c\equiv a+b\pmod{2021}$, then $f(c)\equiv f(a)+f(b)\pmod{2021}$.
- (i) If $f(a)=a$, then $a=0$.
- (ii) If $f(a)=f(b)$, then $a=b$.
- (iii) If $c\equiv a+b\pmod{2021}$, then $f(c)\equiv f(a)+f(b)\pmod{2021}$.