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State True or False. $$2011^{64} + 64$$ is a composite number.
Correct Answer: True
With $$a = 2011^{16}$$, the number is $$a^4 + 4 \times 2^4$$. By Sophie Germain's identity $$a^4 + 4b^4 = (a^2 + 2b^2 + 2ab)(a^2 + 2b^2 - 2ab)$$ with $$b = 2$$, and both factors exceed 1. So it is composite and the statement is True.
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