Definition:Amicable Pair/Historical Note

Historical Note on Amicable Pair

Amicable pairs are on record as having been studied by the Pythagoreans.

The first mathematician to explore amicable pairs systematically was Leonhard Paul Euler.

He published a list of $64$ examples.

There are now over $40 \, 000$ amicable pairs now known, including all such pairs where the smaller pair is under $1 \, 000 \, 000$.

Techniques for generating new amicable pairs from existing ones strongly suggest that there is an infinite number of them, but this still has to be rigorously proven.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $220$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $220$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): amicable numbers
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): amicable numbers
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): amicable numbers