For convenience in typing, call the numeric portion of RHS 'A'.
xyAxAy=0 and (xA)(yA)=A^2
Let k = the amount x differs from A so that x=A+k.
Then (A+k)*y=A*(A+k+y) and y=(A^2)/k + A.
So every factor of A^2 gives a solution. Since A^2 = 2^4*3^8*5^14 there are 5*9*15 = 675 factors. But x and y can be swapped which adds a factor of 2. In addition, x=y=2A is double counted so the number of solutions is 2*6751=1349.

Posted by xdog
on 20190518 19:39:16 