MathDB

A quadratic number is a real root of the equations

ax^2 + bx + c = 0

where

|a|,|b|,|c|\in\{1,2,\ldots,10\}

. Find the smallest positive integer

n

for which at least one of the intervals\left(n-\dfrac{1}{3}, n\right) \text{and} \left(n, n+\dfrac{1}{3}\right)does not contain any quadratic number.

5