?

Number Theory

Free Version

Upgrade subject to access all content

Easy

Additional Applications of Bézout's Identity

NUMTH-S2S$Z7

Which of the following are TRUE?

Select ALL that apply.

A

There exist $a_1, a_2 \in \mathbb{Z}$ such that $-45a_1 + 5a_2 = -9$.

B

There exist $b_1, b_2 \in \mathbb{Z}$ such that $100b_1 + 15b_2 = 2$.

C

There exist $c_1, c_2 \in \mathbb{Z}$ such that $36c_1 + 24c_2 = 12$.

D

There exist $d_1, d_2 \in \mathbb{Z}$ such that $7d_1 + 14d_2 = 3$.