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(p-1)/p cannot be a sum of distinct unit fractions

Source: Singapore Junior Math Olympiad 2006 2nd Round p2 SMO

March 25, 2020
number theorySumFractions

Problem Statement

The fraction 23\frac23 can be eypressed as a sum of two distinct unit fractions: 12+16\frac12 + \frac16 . Show that the fraction p−1p\frac{p-1}{p} where p≥5p\ge 5 is a prime cannot be expressed as a sum of two distinct unit fractions.
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