Timeline for Was Fermat's Last Theorem known for infinitely many primes before Wiles?
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| when toggle format | what | by | license | comment | |
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| 4 hours ago | comment | added | David E Speyer | @tomasz If there were a contest with a prize for the first person to prove FLT for infinitely many primes, then you would definitely have to use interpretation (2) in order to avoid silly arguments of this sort. But as a question about what results were published in the actual history of math, I think both interpretations are reasonable. | |
| 5 hours ago | comment | added | tomasz | @DavidESpeyer: I think it's a bit of a subtle distinction. One might "prove" FLT for infinitely many primes as follows: let $P$ be the set of primes for which FLT holds. Then, provided $P$ is infinite, it follows that FLT holds for infinitely many primes. | |
| 6 hours ago | answer | added | Alexandre Eremenko | timeline score: 2 | |
| 7 hours ago | history | became hot network question | |||
| 13 hours ago | answer | added | Pace Nielsen | timeline score: 9 | |
| 13 hours ago | comment | added | Alison Miller | @Guruprasad: No, Germain only proved the first case of FLT for Sophie Germain primes (as well as for some other primes): see mathwomen.agnesscott.org/women/germain-FLT/SGandFLT.htm for a detailed description of her contributions | |
| 13 hours ago | history | edited | Wojowu | CC BY-SA 4.0 |
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| 13 hours ago | comment | added | Wojowu | @AchimKrause When investigating FLT for exponent $p$, it is for a number of reasons helpful to separate the cases where $p\nmid xyz$, so called first case which is almost always easier, and $p\mid xyz$, which is harder. Fouvry et al. have shown that there are infinitely many primes for which FLT holds under the assumption we are in the first case. The last sentence is written confusingly, but I'm assuming OP just means that FLT holds for exponent $p$ without that assumption. | |
| 13 hours ago | comment | added | Fedor Petrov | @AchimKrause first case is when $p$ does not divide $xyz$. So, the result was that there exist infinitely many primes $p$ for which there are no first case solutions | |
| 13 hours ago | comment | added | Achim Krause | What does "the first case of the equation holds for infinitely many primes p" mean exactly, and why is it not an answer to the question you ask in the second sentence? | |
| 14 hours ago | comment | added | Wojowu | Some time in the past I have tried to look for an answer to this question, and have turned out empty handed. It definitely appears to not have been known, but I have not found in print an explicit mention of that. | |
| 14 hours ago | history | edited | Wojowu | CC BY-SA 4.0 |
added 18 characters in body; edited title
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| 14 hours ago | comment | added | Guruprasad | If there are Infinitely many Sophie Germain primes( Its Still a conjecture). Sophie Germain was first who proved FLT for Infinitely many primes. | |
| 14 hours ago | comment | added | David E Speyer | You need to distinguish between (1) a set $P$ of primes for which FLT was proved and which is probably infinite and (2) a set $P$ of primes for which FLT was known and which was proved to be infinite. Kummer proved FLT for regular primes, and it is conjectured that there are infinitely many regular primes, but it hasn't been proved that there are infinitely many. | |
| 15 hours ago | history | asked | Euro Vidal Sampaio | CC BY-SA 4.0 |