MathDB

Show that the set

S

of natural numbers

n

for which

\frac{3}{n}

cannot be written as the sum of two reciprocals of natural numbers (

S =\left\{n |\frac{3}{n} \neq \frac{1}{p} + \frac{1}{q} \text{ for any } p, q \in \mathbb N \right\}

) is not the union of finitely many arithmetic progressions.

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