NL-NWO 1975 Problem 1

Are the following statements true? $x^7 \in Q \land x^{12} \in Q \Rightarrow x \in Q$ , and $x^9 \in \land x^{12} \in Q \Rightarrow x \in Q$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.