Basic questions about pythagorean triples and "n-lets" I've had some difficulties finding answer to the two following questions:
1) Given one of natural numbers $a,b$ where $b$ is even and $a^2+b^2=c^2$ is there only one such a pythagorean triple? 
2)How about a sum of $n$ squares of natural numbers that is equal to a square of a natural number? Given one of the summed squares is there only one such a pythagorean "n-let"?
 I know that $a$ and $c$ are odd and I am aware of Euclid's formula but I don't know how to use it. I have no idea how to tackle 2). I only know that for exemple of $n=4$ there may be or not such two summed squares that would be lengths of the legs of a right triangle. Perhaps this is trivial but I don't know what to do. 
Edit: 3) How about a given $c$ instead of $a,b$ in 1)?

Question $1$ appears to follow from the two variable equivalent expression:
$$a^2+b^2=c^2, b\in 2k, a,b,c,k \in \Bbb Z $$
$$\to (p^2-q^2)^2 + (2pq)^2=(p^2+q^2)^2, p,q\in \Bbb Z $$
