23.6. (England, 80). Find at least one set $M$ consisting of 7 consecutive natural numbers, for which there exists a polynomial $P(x)$ of the fifth degree with the following properties:

a) all coefficients of the polynomial $P(x)$ are integers;

b) for five numbers $k \in M$, including the smallest and largest numbers, the equality $P(k)=k$ holds;

c) $P(k)=0$ for one number $k \in M$.
23.6. The set $M=\{25 ; 26 ; 27 ; 28 ; 29 ; 30 ; 31\}$ and the polynomial $P(x)=x+(x-25)(x-27)(x-28)(x-29)(x-31)$ satisfy all the conditions of the problem (in this case, condition b) is satisfied for $k=25,27,28$, 29,31, and condition c) - for $k=30$ ).