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  2. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    As an illustration of this, the parity cycle (1 1 0 0 1 1 0 0) and its sub-cycle (1 1 0 0) are associated to the same fraction ⁠ 5 / 7 ⁠ when reduced to lowest terms. In this context, assuming the validity of the Collatz conjecture implies that (1 0) and (0 1) are the only parity cycles generated by positive whole numbers (1 and 2 ...

  3. Lothar Collatz - Wikipedia

    en.wikipedia.org/wiki/Lothar_Collatz

    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.

  4. Gauss circle problem - Wikipedia

    en.wikipedia.org/wiki/Gauss_circle_problem

    Gauss's circle problem asks how many points there are inside this circle of the form (,) where and are both integers. Since the equation of this circle is given in Cartesian coordinates by x 2 + y 2 = r 2 {\displaystyle x^{2}+y^{2}=r^{2}} , the question is equivalently asking how many pairs of integers m and n there are such that

  5. List of conjectures - Wikipedia

    en.wikipedia.org/wiki/List_of_conjectures

    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 ...

  6. Wikipedia:Reference desk/Archives/Mathematics/2009 October 2 ...

    en.wikipedia.org/wiki/Wikipedia:Reference_desk/...

    1.1 Collatz conjecture. 8 comments. ... 1.3 Achilles numbers: Never consecutive? 8 comments. 1.4 Question about shoelaces. 9 comments. Toggle the table of contents.

  7. List of unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    The perfect 1-factorization conjecture that every complete graph on an even number of vertices admits a perfect 1-factorization. Cereceda's conjecture on the diameter of the space of colorings of degenerate graphs [87] The Earth–Moon problem: what is the maximum chromatic number of biplanar graphs? [88]

  8. Marijn Heule - Wikipedia

    en.wikipedia.org/wiki/Marijn_Heule

    Marienus Johannes Hendrikus Heule (born March 12, 1979, at Rijnsburg, The Netherlands) [1] [2] is a Dutch computer scientist at Carnegie Mellon University who studies SAT solvers. Heule has used these solvers to resolve mathematical conjectures such as the Boolean Pythagorean triples problem , Schur's theorem number 5 , and Keller's conjecture ...

  9. Dividing a circle into areas - Wikipedia

    en.wikipedia.org/wiki/Dividing_a_circle_into_areas

    The lemma establishes an important property for solving the problem. By employing an inductive proof, one can arrive at a formula for f(n) in terms of f(n − 1).. Proof. In the figure the dark lines are connecting points 1 through 4 dividing the circle into 8 total regions (i.e., f(4) = 8).