Help showing this is an equivalence relation

Question

I need help with question as following:

1. $X= \mathbb{Z}\times \mathbb{Z}$ I need to define the relation $R$ on $X$ as follows:

   $(X_1,X_2)R(Y_1,Y_2) \longleftrightarrow (X_1)^2+(X_2)^2=(Y_1)^2+(Y_2)^2$

Can you prove it using (X)R(Y) ?

Answer 1

Hint: For describing the equivalence class, think about using cross-multiplication to determine if two fractions are equal.