Challenge questions from FPM quizzes: First quiz on prime factorization

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My third FPM quiz last autumn was on prime factorization. As usual the final question was labelled as a "challenge question". This one is probably relatively easy once you really understand the definition of the set \(S\), which is closely related to the material from my classes on Bézout's lemma. (But you don't need to know about Bézout's lemma to answer the question.)

Here is a screenshot of the question. As usual, the buttons don't do anything, but you can enlarge the image by clicking on it.

Note that three of the statements are true and one of the statements is false. You are supposed to spot the false one!

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