Problem of the Week

PROBLEM 219

Let a₁, a₂, a₃, a₄ be distinct prime numbers.  There are five complex fractions that can be built using these numbers in order, from top to bottom.

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These can be simplified to the simple fractions (a₁a₃ )/(a₂ a₄) , (a₁a₃a₄)/a₂ , (a₁a₄)/(a₂a₃) , (a₁a₃ )/(a₂ a₄),  a₁/(a₂a₃a₄).  Note the first and fourth yield the same simple fractions; so there are, in fact, only four distinct simple fractions that can be built.  

You many distinct simple fractions can you build with the six prime numbers a₁, a₂, a₃ , a₄, a₅, a₆ ?

For the fraction-fearless:  The same question for n distinct prime numbers.

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ã2005 Alberto L. Delgado