MathDB

6

Part of 2009 Baltic Way

Problems(1)

Coefficient of a cubic equations

Source: Baltic Way 2009

12/4/2009
Let a a and b b be integers such that the equation x^3\minus{}ax^2\minus{}b\equal{}0 has three integer roots. Prove that b\equal{}dk^2, where d d and k k are integers and d d divides a a.
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