Primes (fractions) that cannot be expressed as the sum of two distinct unit fractions
Solution 1:
HINT: The largest number, on the one hand, that is less than $1$ that can be written as a sum of $2$ uniform fractions is $\frac{1}{2}+\frac{1}{3} = \frac{5}{6}$. All numbers of the form $\frac{p-1}{p}$ for $p >5$, on the other hand, are in the interval $[\frac{6}{7},1)$. Can you finish from there.