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The Collatz conjecture [a] is one of the most famous unsolved problems in mathematics.
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.
The uniqueness conjecture for Markov numbers [157] that every Markov number is the largest number in exactly one normalized solution to the Markov Diophantine equation. Pillai's conjecture: for any ,,, the equation = has finitely many solutions when , are not both .
A refresher on the Collatz Conjecture: It’s all about that function f(n), shown above, which takes even numbers and cuts them in half, while odd numbers get tripled and then added to 1. Take any ...
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 .
Once known as the "Weil conjecture". 2001: Mark Haiman: n! conjecture: representation theory: 2001: Daniel Frohardt and Kay Magaard [17] Guralnick–Thompson conjecture: monodromy groups: 2002: Preda Mihăilescu: Catalan's conjecture, 1844: exponential diophantine equations: ⇐Pillai's conjecture⇐abc conjecture Mihăilescu's theorem 2002
For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1.2 × 10 12 (1.2 trillion). However, the failure to find a counterexample after extensive search does not constitute a proof that the conjecture is true—because the conjecture might be false but ...
He is known for the Terras theorem about the Collatz conjecture, published in 1976, [6] which proved that the conjecture holds for "almost all" numbers and established bounds for the conjecture. [7] [8] He married fellow mathematician Audrey Terras. [9]