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Number Theory

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Applying Bézout's Identity to Two Nonzero Integers

NUMTH-NXKCHR

Which of the following statements are TRUE?

A

There exist $w_1, w_2 \in \mathbb{Z}$ such that $6w_1 + 3w_2 = 5$.

B

There exist $x_1, x_2 \in \mathbb{Z}$ such that $6x_1 + 3x_2 = 2$.

C

There exist $y_1, y_2 \in \mathbb{Z}$ such that $6y_1 + 3y_2 = 3$.

D

There exist $z_1, z_2 \in \mathbb{Z}$ such that $6z_1 + 3z_2 = 1$.