Condition for roots of a quadratic be integers

09232010, 05:36 PM
Post: #1




Condition for roots of a quadratic be integers
Let $ m$ and $ n$ be positive integers such that $ x^2  mx + n = 0$ has real roots $ \alpha$ and $ \beta$.
Prove that $ \alpha$ and $ \beta$ are integers if and only if $ \left\lfloor m\alpha \right \rfloor + \left\lfloor m\beta \right\rfloor$ is the square of an integer. 

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