Erdős-Straus Conjecture

Unproven Hypothesis

Let $n$ be an integer.

It is conjectured that $\dfrac 4 n$ can always be expressed as the sum of $3$ unit fractions.

Sierpiński Variant

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 Paul Erdős and Ernst Gabor Straus.

Sources

• 1950: Paul Erdős: Az $1 / x_1 + 1 / x_2 + \cdots + 1/x_n = a / b$ egyenlet egész számú megoldásairól (On a Diophantine Equation) (Mat. Lapok Vol. 1: pp. 192 – 210)

• 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): $2 / 3$