142. Find a 7-arithmetic fractional-linear function $f(x)$ such that $f(0)=0, f(1)=4, f(4)=2$.

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142. The desired function is $f(x)=\frac{x}{2}$. We can find it in the following way. Let's write $f(x)$ in the general form

$$
f(x)=\frac{a x+b}{c x+d}
$$

and substitute $0, 1, 4$ for $x$ sequentially. Solving the equations for $a, b, c, d$

$$
\left\{\begin{array}{l}
\frac{a \cdot 0+b}{c \cdot 0+d}=0 \\
\frac{a \cdot 1+b}{c \cdot 1+d}=4 \\
\frac{a \cdot 4+b}{c \cdot 4+d}=2
\end{array}\right.
$$

we get that $b=d=0, c=2 a$ and, consequently, the desired function is $f(x)=\frac{a x}{2 a x}=\frac{x}{2}$.