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I read this answer to this question on MathOverflow, and I enjoyed reading the proof given in the linked paper, but... where is the mistake? I know nothing of the Mason-Stothers Theorem except its statement and truth, and the reasoning in the paper seems to be logically sound to me.

Intuitively, I feel that the result obtained (that there cannot exist complex polynomials with the given conditions) does not actually imply the statement of Fermat's Last Theorem (which deals with positive integers), though I cannot justify this. Could anyone explain the flaw in the proof?

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It's a dumb trick; the author's just misstating the Mason-Stothers theorem, which includes the condition that the three polynomials are relatively prime. Here the polynomials are all multiples of $t$ so they aren't relatively prime.

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    $\begingroup$ Thank you for pointing that out. However, the third example on the Mason-Stothers Theorem's Wikipedia page is still true for relatively prime polynomials, right? $\endgroup$ – shardulc Apr 2 '16 at 8:46
  • $\begingroup$ @shardulc: yes, but it just doesn't imply FLT over the integers. $\endgroup$ – Qiaochu Yuan Apr 2 '16 at 9:01

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