Egyptian Fractions Calculator

An Egyptian fraction is the sum of distinct unit fractions (fractions with a numerator of 1). For example, \( \frac{2}{5} = \frac{1}{3} + \frac{1}{15} \).

This calculator uses the greedy algorithm (Fibonacci-Sylvester method) to decompose a proper fraction into its Egyptian fraction representation.

Steps of the Algorithm:

1. Start with the fraction you want to decompose, e.g., \(\frac{a}{b}\).
2. Find the smallest integer \(x\) such that \(\frac{1}{x} \le \frac{a}{b}\). This is calculated as \(x = \lceil \frac{b}{a} \rceil\). This is the first unit fraction.
3. Subtract this unit fraction from the original fraction: \(\frac{a}{b} - \frac{1}{x}\).
4. If the result is not zero, repeat the process with the new fraction.

Disclaimer: This calculator is for educational purposes only. While we strive for accuracy, please verify all results for critical applications.