# $$\mathfrak{Square}^{\mathfrak{Square}}$$

Level pending

The squares 1, 25, 49 are pairwise relatively prime and in arithmetic progression. Let $$x_1^2, y_1^2, z_1^2$$ and $$x_2^2, y_2^2, z_2^2$$ be the next two smallest triples with this property when value is measured by the $$z_n$$'s. Find $$z_1+z_2$$.

Note: This problem is not original.

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