Easy# Linear Diophantine Equations with Three Variables

NUMTH-HRHDF1

Let $a, b, c, d \in \mathbb{Z}$. Then, the equation $ax + by + cz = d$ has infinitely many integral solutions if $\gcd(a, b, c) | d$ and no solutions if $\gcd(a, b, c) \nmid d$.

Which of the following equations have infinitely many integral solutions? Select **ALL** that apply.