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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 ...
A generalized version of the conjecture states that, for any positive , all but finitely many fractions can be expressed as a sum of three positive unit fractions. The conjecture for fractions 5 n {\displaystyle {\tfrac {5}{n}}} was made by Wacław Sierpiński in a 1956 paper, which went on to credit the full conjecture to Sierpiński's student ...
The Erdős–Heilbronn conjecture in combinatorial number theory on the number of sums of two sets of residues modulo a prime, proved by Dias da Silva and Hamidoune in 1994. [11] The Erdős–Graham conjecture in combinatorial number theory on monochromatic Egyptian fraction representations of unity, proved by Ernie Croot in 2000. [12]
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.
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 {}.
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 .
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. [1] [2] [3] Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to ...
This conjecture is known as Lemoine's conjecture and is also called Levy's conjecture. The Goldbach conjecture for practical numbers, a prime-like sequence of integers, was stated by Margenstern in 1984, [33] and proved by Melfi in 1996: [34] every even number is a sum of two practical numbers.