One leg of a PT will always be divisible by 3, and one (possibly the same leg) will always be divisible by 4 so area will be divisible by 6.
Since the sum of the digits = 45, only 0,3,6,9 can be the omitted digit.
Using the parametric solution for primitive solutions, x=2ab and y=a^2b^2 with (a,b) relatively prime and of opposite parity. Then area = ab(a+b)(ab), the product of four relatively prime numbers.
For nonprimitive solutions the legs are scaled by a common factor so area will be divisible by a square.
None of this points to a solution, not to me anyway, but at least it limits the search space.

Posted by xdog
on 20171118 07:37:04 