I have encountered the following question in my textbook:
Let $P(x)=x^4+ax^3+bx^2+cx+d$. If $P(1) = 1, P(2)=8, P(3)=27, P(4)=64$, then the value of $P(5)$ divisible by a prime number is ____
I have solved the problem and obtained $P(5)=149$. However, the answer as mentioned in the textbook is $3$. I believe that this has something to do with the final statement: divisible by a prime number.
According to my understanding, every integer is divisible by 1 and one or more prime numbers. A prime number is divisible only by itself and 1. What does divisible by a prime number mean in this context, and how does it convert 149 to 3?