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Curious Real Additive Relationship (Posted on 20080412) 

Are there any non zero real triplet(s) (p, q, r) that satisfy the following system of equations?
p + 1/p = q, q + 1/q = r, and r + 1/r = p
If such triplet(s) exist, find at least one of these. Otherwise, prove that no such triplet can conform to the given conditions.
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