## Heronian triangles with one side Even of length a = 4,6,8,10 –(Part 2)

There are infinitely many of primitive Heronian triangles with one side of length   a > 2

If   $a$   is even:     two cases

(1)

If   $a$   is even, say   $a = 2 \, n$,   where $n$ is odd.

we may use

$a$,      $t \, n \; - \; 2$,      $t \, n \; + \; 2$

where   $t$   is a solution of the Pelian equation

$t^2 \; - \; (n^2 - 4) \, y^2 \; = \; 1$

(2)

If   $a = 2 \,n$   where   $n$   is even

we may use

$a$,      $t \, n \; - \; 1$,      $t \, n \; + \; 1$

where   $t$   is a solution of the Pelian equation

$t^2 \; - \; (n^2 - 1) \, y^2 \; = \; 1$

Here are the first few solutions: