1. For which $a$
1) the equation $f(f(x))=x$ has an infinite number of solutions;
2) the equation $f(f(f(f(x))))=x$ has an infinite number of solutions for the function of the form

$$
f(x)=\frac{(5-3 a) x-2}{5 x+a-1} ?
$$
Answer: 1) $a=2, f(x)=\frac{-x-2}{5 x+1}$
2) $a=2, f(x)=\frac{-x-2}{5 x+1} ; a=3, f(x)=\frac{-4 x-2}{5 x+2}$

$$
a=\frac{1}{5}, f(x)=\frac{22 x-10}{25 x-4}
$$