21. Let $m>1, c \geqslant 1, (a, m)=1$; and let $\delta_{m}\left(a^{c}\right)=d$. Try to determine the condition that $\delta_{m}(a)$ should satisfy and the number of possible values it can take.
21. $\delta_{m}(a)=\left(\delta_{m}(a), c\right) \cdot d$.

Translates to:

21. $\delta_{m}(a)=\left(\delta_{m}(a), c\right) \cdot d$.