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SMO 2006 Junior Round 2 Question 2

SMO · SMO 2006 Junior Round 2

Question 2

The fraction $\frac 23$ can be expressed as a sum of two distinct unit fractions: $\frac 12+\frac 16$. Show that the fraction $\frac{p-1}{p}$, where $p\ge 5$ is a prime, cannot be expressed as a sum of two distinct unit fractions.