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State True or False. If $$x$$ and $$y$$ are perfect squares and $$y = x + 1$$ then number of such ordered pairs $$(x, y)$$ is more than 1
Correct Answer: False
If $$x = a^2$$ and $$y = b^2$$ with $$a, b \ge 0$$, then $$(b - a)(b + a) = 1$$, so $$b - a = b + a = 1$$, giving $$a = 0$$ and $$b = 1$$. The only pair is $$(0, 1)$$, so there is not more than one such pair, and the statement is False.
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