Pythagorean Triples

Definition:

http://en.wikipedia.org/wiki/Pythagorean_triple

http://mathworld.wolfram.com/PythagoreanTriple.html

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Pythag/pythag.html

Notice any patterns?

http://www.math.uic.edu/~fields/puzzle/triples.html

Primitive Pythagorean Triangle are given by
a = m^2 + n^2
b = 2mn
c = m^2 - n^2
where m and n are of opposite parity and are relatively prime.

(1)

Find a primitive Pythagorean Triangle with one leg of the form xyyxyy and an area that is a permutation of the nine nonzero digits

(2)

The generators m = 365 and n = 338 lead to a primitive Pythagorean Triangle with a pandigital area, 2341685970, where the first three digits are consecutive in order.
Find the other primitive Pythagorean Triangle with the same characteristics.

(3)

Are there Pythagorean Triangles whose perimeters equal their areas?

(4)

Can two different primitive Pythagorean Triangle with sides (a, b, c) and (r, s, t) be such

a*b*c = r*s*t ?