Mordellās conjecture
Quick Summary
Mordell's conjecture, now known as Faltings's theorem, is a significant result in algebraic geometry and number theory. It states that for a given algebraic curve defined by polynomial equations with rational coefficients, if the genus of the curve is greater than or equal to two, then there are only a finite number of rational solutions with no common factors.1
This theorem implies that certain types of polynomial equations, such as (x^n + y^n = z^n) for (n > 2), have a limited number of integer solutions. The conjecture was proven by German mathematician Gerd Faltings in 1983, a feat that earned him the Fields Medal. The proof unified aspects of arithmetic and algebraic geometry, demonstrating the power of abstract mathematical theories to solve concrete problems.12
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Gerd Faltingsā¦for his proof of the Mordell conjecture. In 1922 Louis Mordell had conjectured that a system of algebraic equations with rational coefficients that defines an algebraic curve of genus greater than or equal to two (a surface with two or more āholesā) has only a finite number of rational solutionsā¦
Read Moreā¦for his proof of the Mordell conjecture. In 1922 Louis Mordell had conjectured that a system of algebraic equations with rational coefficients that defines an algebraic curve of genus greater than or equal to two (a surface with two or more āholesā) has only a finite number of rational solutionsā¦
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mathematicsDevelopments in pure mathematicsā¦he solved the Englishman Louis Mordellās conjecture in 1983. This conjecture states that almost all polynomial equations that define curves have at most finitely many rational solutions; the cases excluded from the conjecture are the simple ones that are much better understood.
Read Moreā¦he solved the Englishman Louis Mordellās conjecture in 1983. This conjecture states that almost all polynomial equations that define curves have at most finitely many rational solutions; the cases excluded from the conjecture are the simple ones that are much better understood.
Read More