เราอาจพิสูจน์ทฤษฎีบทนี้ในกรณีที่ n = 4 และกรณีที่ n เป็นจำนวนเฉพาะ ก็สามารถสรุปได้ว่าทฤษฎีบทเป็นจริงสำหรับทุกค่า n.
แฟร์มาได้พิสูจน์กรณี n = 4, ออยเลอร์ พิสูจน์กรณี n = 3, ดิลิชเลต และ เลอจองดร์ พิสูจน์กรณี n = 5 เมื่อ ค.ศ. 1828, Gabriel Lamé พิสูจน์กรณี n = 7 เมื่อ ค.ศ. 1839
ใน ค.ศ. 1983 Gerd Faltings ได้พิสูจน์ข้อความคาดการณ์ของ Mordell สำเร็จ ซึ่งกล่าวว่าสำหรับ n > 2 จะมีจำนวนเต็ม a, b และ c ซึ่งเป็นจำนวนเฉพาะสัมพัทธ์กัน และทำให้ an + bn = cn อยู่จำนวนจำกัด
Cubum autem in duos cubos, aut quadrato-quadratum in duos quadrato-quadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exigitas non caperet.
I don’t believe Fermat had a proof. I think he fooled himself into thinking he had a proof. But what has made this problem special for amateurs is that there’s a tiny possibility that there does exist an elegant seventeenth century proof.
Weisstein, Eric W. "Fermat's Last Theorem". mathworld.wolfram.com (ภาษาอังกฤษ).
↑ Wiles, Andrew (May 1995). "Modular Elliptic Curves and Fermat's Last Theorem". The Annals of Mathematics. 141 (3): 443. doi:10.2307/2118559.
"The Abel Prize Laureate 2016". www.abelprize.no.
Stewart, Ian; Tall, David. Algebraic Number Theory and Fermat's Last Theorem. CRC PRESS. ISBN9780367658717.
"Shimura-Taniyama conjecture - Encyclopedia of Mathematics". encyclopediaofmath.org.
Stillwell, John. Mathematics and its history : a concise edition. Springer. p. 210-211. ISBN978-3-030-55192-6.
"NOVA Online | The Proof | Solving Fermat: Andrew Wiles". www.pbs.org.
ดูเพิ่ม
Stewart, Ian; Tall, David. Algebraic Number Theory and Fermat's Last Theorem. CRC PRESS. ISBN9780367658717.
Saitō, Takeshi. Fermat’s Last Theorem: The Proof. Providence, Rhode Island: American Mathematical Society. ISBN978-0-8218-9849-9.
"Fermat's last theorem". Encyclopedia of Mathematics.
สิงหาคม 16, 2021
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