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The conjecture is that there is a simple way to tell whether such equations have a finite or infinite number of rational solutions. More specifically, the Millennium Prize version of the conjecture is that, if the elliptic curve E has rank r , then the L -function L ( E , s ) associated with it vanishes to order r at s = 1 .
Serre's multiplicity conjectures: commutative algebra: Jean-Pierre Serre: 221 Singmaster's conjecture: binomial coefficients: David Singmaster: 8 Standard conjectures on algebraic cycles: algebraic geometry: n/a: 234 Tate conjecture: algebraic geometry: John Tate: Toeplitz' conjecture: Jordan curves: Otto Toeplitz: Tuza's conjecture: graph ...
Homological conjectures in commutative algebra; Jacobson's conjecture: the intersection of all powers of the Jacobson radical of a left-and-right Noetherian ring is precisely 0. Kaplansky's conjectures; Köthe conjecture: if a ring has no nil ideal other than {}, then it has no nil one-sided ideal other than {}.
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
The proof has appeared in "Annals of Mathematics" in March 2019. [5] The Burr–Erdős conjecture on Ramsey numbers of graphs, proved by Choongbum Lee in 2015. [6] [7] A conjecture on equitable colorings proven in 1970 by András Hajnal and Endre Szemerédi and now known as the Hajnal–Szemerédi theorem. [8]
The Collatz conjecture states that all paths eventually lead to 1. The Collatz conjecture [a] is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1.
Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers .
The conjecture is named after Paul Erdős and Ernst G. Straus, who formulated it in 1948, but it is connected to much more ancient mathematics; sums of unit fractions, like the one in this problem, are known as Egyptian fractions, because of their use in ancient Egyptian mathematics. The Erdős–Straus conjecture is one of many conjectures by ...