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x^7 \in Q \land x^{12} \in Q => x \in Q

Source: Netherlands - Dutch NMO 1975, year 1975-76 (also named as 1975 -2) p1

January 27, 2023
algebra

Problem Statement

Are the following statements true?
x7∈Q∧x12∈Q⇒x∈Qx^7 \in Q \land x^{12} \in Q \Rightarrow x \in Q, and x9∈∧x12∈Q⇒x∈Qx^9 \in \land x^{12} \in Q \Rightarrow x \in Q.
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