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.

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.