MathDB

3

Part of 2007 India National Olympiad

Problems(1)

Prove that the roots of a quadratic are integers

Source: INMO 2007 Question 3

11/2/2009
Let m m and n n be positive integers such that x^2 \minus{} mx \plus{}n \equal{} 0 has real roots α \alpha and β \beta. Prove that α \alpha and β \beta are integers if and only if [m\alpha] \plus{} [m\beta] is the square of an integer. (Here [x] [x] denotes the largest integer not exceeding x x)
quadraticsinequalitiesnumber theory unsolvednumber theory