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3

Part of 1983 Dutch Mathematical Olympiad

Problems(1)

real numbers

Source: Netherlands 1983

6/27/2009
Suppose that a,b,c,p a,b,c,p are real numbers with a,b,c a,b,c not all equal, such that: a\plus{}\frac{1}{b}\equal{}b\plus{}\frac{1}{c}\equal{}c\plus{}\frac{1}{a}\equal{}p. Determine all possible values of p p and prove that abc\plus{}p\equal{}0.
algebra unsolvedalgebra