An algebra problem by Rahil Sehgal

$x^2 - nx + 2014 = 0 \\ \text{To have integer roots, discriminant must be a perfect square} \\ n^2 - 4 \times 2014 = x^2 \\ n^2 - 8056 = x^2 \\ \text{Clearly, } n^2 > 8056 \\ \implies n > 89.7552226893 > 90 \\ \text{Using trail and error method, at first change using n = 91 } \\ n^2 = 91^2 = 8281 \\ \implies n^2 - 8056 = 8281 - 8056 = 25 = 5^2 \\ \boxed{\therefore n = 91, \text{ is the smallest possible value for 'n' for which the equation has integral roots}}$