• 0 Votes - 0 Average
• 1
• 2
• 3
• 4
• 5
 Condition for roots of a quadratic be integers
09-23-2010, 05:36 PM
Post: #1
 elim Moderator Posts: 577 Joined: Feb 2010 Reputation: 0
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.
 « Next Oldest | Next Newest »

Forum Jump: