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State True or False. If $$a$$, $$b$$ are integers such that $$a^2 + b^2 = 29$$ then the maximum value of $$|a - b| = 3$$
Correct Answer: False
The only way to write 29 as a sum of two squares is $$4 + 25$$, so $$\{|a|, |b|\} = \{2, 5\}$$. Taking $$a = 5$$, $$b = -2$$ gives $$|a - b| = 7$$, which is the maximum. So the statement is False.
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