Answer Happy

1. If x, y, and z are relatively prime integers such that
x^2 +y^2 +λy = z^2, λ = 2β, and x < y, then x is even, y
and z are odd when β is even and n is odd.
2. If x, y, and z are relatively prime integers such that
x^2 +y^2 +λy = z^2, λ = 2β, and x < y, then x and z are
odd and y is even when β is even and n is zero and
even.
1. If x, y, and z. are relatively prime integers such that x² + y² + 2y = z², λ = 2ß, and x < y, then x is even, y and z are odd when ß is even and n is odd. 2. If x, y, and z are relatively prime integers such that x² + y² + λy=z², λ = 2ß, and x < y, then x and z are odd and y is even when ß is even and n is zero and even.