438*. What remainder does $46^{925}$ give when divided by $21?$
$\triangle$ The solution method we applied in the last problems is too cumbersome here due to the large base of the exponent and the large divisor. Let's try to modify it.

Divide 46 by 21 with a remainder and transform the exponent:

$$
46^{925}=(21 \cdot 2+4)(21 \cdot 2+4) \ldots(21 \cdot 2+4)
$$

If we multiply 925 identical sums together, then all the terms in the resulting sum are divisible by 21, except for the term $4^{925}$. Therefore, the remainder of the division of the power $46^{925}$ by 21 coincides with the remainder of the division of the power $4^{925}$ by 21.

Let's use the fact that

$$
4^{3}=64=21 \cdot 3+1
$$

We get:

$4^{925}=4 \cdot 4^{924}=4 \cdot\left(4^{3}\right)^{308}=4 \cdot 64^{308}=4 \cdot(21 \cdot 3+1)^{308}=4 \cdot(21 k+1)=4 \cdot 21 k+4$.

Therefore, the desired remainder is 4.

Answer: 4.