Question 149
Find the smallest positive integer $N$ with the following property:
For any degree five polynomial $P(x)$ with integer coefficients, there is $0 \le x \le 1$ such that $|P(x)| \gt \frac{1}{N}$.
For any degree five polynomial $P(x)$ with integer coefficients, there is $0 \le x \le 1$ such that $|P(x)| \gt \frac{1}{N}$.