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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.
The Collatz conjecture [a] is one of the most famous unsolved problems in mathematics.
The most familiar problem with an Erdős prize is likely the Collatz conjecture, also called the 3N + 1 problem. Erdős offered $500 for a solution. Erdős offered $500 for a solution. Collaborators
Of the original seven Millennium Prize Problems listed by the Clay Mathematics Institute in 2000, six remain unsolved to date: [6]. Birch and Swinnerton-Dyer conjecture; Hodge conjecture
Schanuel's conjecture; Schinzel's hypothesis H; Scholz conjecture; Second Hardy–Littlewood conjecture; Serre's conjecture II; Sexy prime; Sierpiński number; Singmaster's conjecture; Safe and Sophie Germain primes; Stark conjectures; Sums of three cubes; Superperfect number; Supersingular prime (algebraic number theory) Szpiro's conjecture
Lothar Collatz (German:; July 6, 1910 – September 26, 1990) was a German mathematician, born in Arnsberg, Westphalia. The "3x + 1" problem is also known as the Collatz conjecture, named after him and still unsolved. The Collatz–Wielandt formula for the Perron–Frobenius eigenvalue of a positive square matrix was also named after him.
Conjecture Field Comments Eponym(s) Cites 1/3–2/3 conjecture: order theory: n/a: 70 abc conjecture: number theory: ⇔Granville–Langevin conjecture, Vojta's conjecture in dimension 1 ⇒Erdős–Woods conjecture, Fermat–Catalan conjecture Formulated by David Masser and Joseph Oesterlé. [1] Proof claimed in 2012 by Shinichi Mochizuki: n/a ...
Lagaria's wild numbers are connected with the Collatz conjecture and the concept of the 3x + 1 semigroup. [2 ... The money prize was now awarded to whoever found a ...