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Solving x > 13874 Abs[x^3 - 3 y^3]
Author

Ed Pegg
Organization: Wolfram Research, Inc.
Department: Scientific Information Group
Description

Since the days of Fermat, it has been an ongoing challenge to find simple-appearing equations with large solutions. The equation in the title seems simple enough, but the smallest solution has 1781 digits. It can be called a Diophantine Inequality. Various methods of continued fractions are discussed.
Subject

*Mathematics > Recreational Mathematics
Keywords

Continued Fraction, Diophantine Inequality
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Abs13874.nb (9.5 KB) - Mathematica Notebook