![]() The unsolved problem stimulated the development of algebraic number theory in the 19th and 20th centuries. It also proved much of the Taniyama–Shimura conjecture, subsequently known as the modularity theorem, and opened up entire new approaches to numerous other problems and mathematically powerful modularity lifting techniques. It was described as a "stunning advance" in the citation for Wiles's Abel Prize award in 2016. After 358 years of effort by mathematicians, the first successful proof was released in 1994 by Andrew Wiles and formally published in 1995. Consequently the proposition became known as a conjecture rather than a theorem. Although other statements claimed by Fermat without proof were subsequently proven by others and credited as theorems of Fermat (for example, Fermat's theorem on sums of two squares), Fermat's Last Theorem resisted proof, leading to doubt that Fermat ever had a correct proof. Fermat added that he had a proof that was too large to fit in the margin. The proposition was first stated as a theorem by Pierre de Fermat around 1637 in the margin of a copy of Arithmetica. ![]() The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions. In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation a n + b n = c n for any integer value of n greater than 2. ![]()
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