Question

What is the smallest possible natural number n for which the equation
${x}^{2} - nx + 2014 = 0$


has integer roots?

Answer 1

If the roots are , , then we have = 2014. As they are integers, , must be
divisors of 2014 = 2 ∙ 19 ∙ 53, giving {, } = {1,2014} {−1, −2014} {2, 1007}
{−2, −1007} {19,106} {−19, −106} {38,53} {−38, −53}. Also = + ,
has the least positive value of as 38 + 53 = 91.

Answer 2

ok it's easy question you can solve it...