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Number Theory

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Moderate

Which Have an Integral Solution?

NUMTH-NC8E3N

Let $a \in \mathbb{N}$. Which of the following equations have an integral solution regardless of the choice of $a$? Select ALL that apply.

A

$ax + a^2y = a^{100}$

B

$ax + (a + 1)y = 3$

C

$a^{2}x + a^{3}y = a - 1$

D

$(a + 1)x + (a - 1)y = 3$