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The 35 pages that link to Fermat's Last Theorem, each with the reason it gives.

• Algebraic number theoryRelated: Attempts to factor equations in cyclotomic integers exposed both the power and limits of ideal methods.

• Elliptic curveRelated: Its proof used elliptic curves and modular forms to rule out a hypothetical counterexample.

• Modular formRelated: The modularity theorem supplied the central bridge in its proof.

• Cyclotomic polynomialRelated: Kummer used arithmetic in cyclotomic fields in a major approach to the theorem.

• Alexander GrothendieckRelated: Modern arithmetic geometry, built partly on Grothendieck’s foundations, informed the route to its proof.

• DiophantusRelated: Fermat's famous marginal note was written in his copy of Diophantus's Arithmetica.

• Schur's theoremRelated: Schur's original motivation was to derive a finite-field consequence of this equation.

• Ernst KummerRelated: Kummer devoted decades to proving this theorem for broad classes of exponents.

• Jean-Pierre SerreRelated: Serre’s modularity conjecture contributed a key route toward the theorem’s eventual proof.

• Sophie GermainRelated: Her partial result influenced later approaches to the theorem, though it did not prove it completely.

• Algebraic integerRelated: Nineteenth-century attempts to prove it drove arithmetic in cyclotomic integer rings.

• Langlands programRelated: Its proof used modularity results connecting elliptic curves and modular forms.

• Modularity theoremRelated: Semistable modularity, combined with Ribet's theorem, yields its proof.

• Infinite descentRelated: Fermat claimed a descent proof for the exponent-four case, a central historical connection.

• Catalan's conjectureRelated: Its history illustrates how exponential Diophantine problems can resist proof for centuries.

• Sophie Germain primeRelated: Germain developed a significant approach to special exponents using properties of primes.

• Andrew WilesRelated: Wiles encountered the problem as a child and later made its proof his central research goal.

• Fermat's right triangle theoremRelated: Both results reflect Fermat's use of descent to prohibit integer solutions.

• Robert LanglandsRelated: Wiles proved it using modularity results arising from the arithmetic of elliptic curves.

• Sophie Germain's identityRelated: Sophie Germain used related factorization ideas in her work toward special cases of the theorem.

• Beal's conjectureRelated: It settles the equal-exponent special case, where Beal's conjecture's bases must share a prime factor.

• Kummer–Vandiver conjectureRelated: Kummer’s cyclotomic approach to this theorem led to class-number questions related to the conjecture.