Definition:Amicable Pair/Historical Note

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Historical Note on Amicable Pair

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

He found over $60$ 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