# Ohh, squares

Two positive integers ($$x, y$$) satisfy that $$xy+1$$ is a perfect square.

True or false?

There always exist a positive integer ($$z$$), where all of the numbers below are perfect squares. \begin{align} yz & + 1 \\ xz & + 1 \\ xy+xz+yz & + 1 \end{align}

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