Stage: 5 Challenge Level: 
The proof depends on the prime factorizations of $a$, $b$, $c$ and $d$.
Mathematical reasoning & proof. Converse of theorem and inverse. Music. Rational and irrational numbers. epsilons. Proof by contradiction. Stage 5 - Reviewed 2012. Factors and multiples. Ratio. Prime factors.
Published November 2006,December 2006.
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