Erdős-Straus Conjecture/Sierpiński Variant

Unproven Hypothesis

Let $n$ be an integer.

It is conjectured that $\dfrac 5 n$ can always be expressed as the sum of $3$ unit fractions.

Source of Name

This entry was named for Wacław Franciszek Sierpiński.

Sources

• 1956: Wacław Sierpiński: Sur les décompositions de nombres rationnels en fractions primaires (Mathesis Vol. 65: pp. 16 – 32)

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2 / 3$
• 1994: Richard K. Guy: Unsolved Problems in Number Theory (2nd ed.)
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2 / 3$