Thabit's Rule/Historical Note

Historical Note on Thabit's Rule

Thabit's Rule has been discovered and rediscovered several times during the course of history.

The first person on record to discuss it was Thabit ibn Qurra, in his Book on the Determination of Amicable Numbers.

The Thabit pair $\tuple {17 \,296, 18 \, 416}$ was discovered by Ibn al-Banna' al-Marrakushi, who may well have also rediscovered this rule.

In $1636$ it was rediscovered by Pierre de Fermat, who also rediscovered the Thabit pair $\tuple {17 \,296, 18 \, 416}$.

At around the same time, René Descartes also rediscovered it, and also rediscovered the Thabit pair $\tuple {9 \, 363 \, 584, 9 \, 437 \, 056}$.

These three remain the only known Thabit pairs.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $220$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $220$