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Integer Roots (Posted on 2006-10-14) Difficulty: 2 of 5
Find all integers n for which the equation x3 - 13x + n = 0 has three integer roots.

See The Solution Submitted by Bractals    
Rating: 2.5000 (2 votes)

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Some Thoughts Some thoughts | Comment 1 of 5
Since the x coefficient is 0, the three roots are p, q, and -(p+q). From the relationship between roots and coefficients, we also know that p.q.(p+q)=n, and pq-p(p+q)-q(p+q)=-13, so p+pq+q=-13. The last one is equivalent to (p-q)/(p-q)=-13... but at first sight I don't see if this can have integer solutions.
  Posted by Federico Kereki on 2006-10-14 16:52:52
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