MathDB

S is not the union of finitely many arithmetic progressions

Source: IMO LongList 1982 - P15

March 16, 2011

modular arithmeticnumber theory unsolvednumber theory

Problem Statement

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.