7.3 It is known that for some natural number $n$ each of the numbers $3 n-1$ and $n-10$ is divisible by a prime number p. Find the number p.
Answer: 29

Solution. The number $3 n-1-3(n-10)=29$ is divisible by p. Since $29$ is a prime number, then $\mathrm{p}=29$.