Parity of Numbers in Amicable Pair

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Open Question

It is not known whether it is possible for the numbers in an amicable pair to have opposite parity.

All known amicable pairs consist of numbers which are either both odd or both even.


If there do exist an amicable pair whose numbers are of opposite parity, then:

the even number is either square or $2$ times a square
the odd number is square.