Definition:Amicable Pair/Historical Note

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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.