Title:
Fermat's Theorem Is Incorrect.

Authors:
Le Thanh Duc, Le Thi Thu Thuy, Viet Nam

Abstract:

Fermat's theorem has existed for a long time, since 1637. Many authors have proposed different proofs. However, no argument has definitively resolved the theorem's validity. In 1995, Andrew Wiles proved the theorem to be true, and this solution has been widely accepted by scientists to this day. The goal of this paper is to prove Fermat's theorem false. Andrew Wiles's argument contains flaws. The paper uses previously established classical mathematical results, highlighting the errors in those concepts. Through this, new knowledge is gained, which is then used to prove and strengthen the argument presented in the paper. The vast body of mathematical knowledge influences and intertwines with itself. Therefore, time is needed for the full impact to be felt. The author of this paper recognizes that, in the process of applying this knowledge, the arguments presented must be logical, consistent, and complete. Therefore, they are highly reliable. At the time this paper was published, no author had refuted them. However, further verification using computer systems is still needed to confirm and solidify their validity. The results of this paper have contributed to basic science and opened up entirely new directions of research and application in mathematics and other related fields.

DOI: http://dx.doi.org/10.51505/ijaemr.2026.11503