2004 Indonesia MO Problems/Problem 6
A quadratic equation with integers and has roots which are positive integers. Prove that is not a prime.
Let and be the two positive roots of the quadratic. By Vieta's Formulas, Square both equations to get Add the two equations to get The right hand side can be factored into . Since , and , so can never be a prime since it can be written as the product of two integers greater than one.
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