189. An integer $a$ is not divisible by 5. Can the number $3 a^{4}+1$ be divisible by 5?
$\triangle$ From the statement of problem 183, it follows that in this case $a^{4}$ when divided by 5 can only leave a remainder of $1: a^{4}=5 k+1(k-$ an integer non-negative). Then

$$
3 a^{4}+1=3(5 k+1)+1=15 k+4
$$

The last sum is not divisible by 5 for any non-negative integer $k$.

Answer: cannot.