update on recent post

[American Citizen <website.reader3@gmail.com>]

To all:

John Ramsden and I have been working on trying to find the suitable 
parameterization for a Heron triangle with all 3 sides square.

There are 2 known examples.

> area: 131674446875520 sides: a,b,c = 4427^2, 4380^2, 1853^2 gcd:1
> area: 1136958242123502720 sides a,b,c = 68595^2, 68104^2 ,11789^2 gcd:1
John determined that

> The actual equations defining a Heronian triangle with all sides 
> square (when scaled by a suitable common factor) are the following 
> simultaneous pair:
>
>   (1)   (a^2 + 1)/a = [ (b^2 + 1)/b ] c^2
>
>   (2)   (1 - a^2)/a + (1 - b^2)/b  = [ (b^2 + 1)/b ] d^2
where a,b,c,d are rationals (in Q)

We are hoping that we might be able to parameterize (1) in particular, 
and use those results in (2) to help find such examples.

I wanted to update the GP Pari community as to our search status

Randall