Common Sum of 3 Distinct Amicable Pairs

Theorem
The integer $64 \, 795 \, 852 \, 800$ is the sum of $3$ distinct amicable pairs:


 * $29 \, 912 \, 035 \, 725$ and $34 \, 883 \, 817 \, 075$


 * $31 \, 695 \, 652 \, 275$ and $33 \, 100 \, 200 \, 525$


 * $32 \, 129 \, 958 \, 525$ and $32 \, 665 \, 894 \, 275$

all of them odd.

Proof
We have that:

From $29 \, 912 \, 035 \, 725$ and $34 \, 883 \, 817 \, 075$ are amicable:

From $31 \, 695 \, 652 \, 275$ and $33 \, 100 \, 200 \, 525$ are amicable:

From $32 \, 129 \, 958 \, 525$ and $32 \, 665 \, 894 \, 275$ are amicable: