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  2. Treaty on the Final Settlement with Respect to Germany

    en.wikipedia.org/wiki/Treaty_on_the_Final...

    The Treaty on the Final Settlement with Respect to Germany ( German: Vertrag über die abschließende Regelung in Bezug auf Deutschland[ a] ), more commonly referred to as the Two Plus Four Agreement ( German: Zwei-plus-Vier-Vertrag[ b] ), is an international agreement that allowed the reunification of Germany in October 1990.

  3. 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 ...

  4. Millennium Prize Problems - Wikipedia

    en.wikipedia.org/wiki/Millennium_Prize_Problems

    e. The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US$ 1 million prize for the first correct solution to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved ...

  5. Fibonacci sequence - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_sequence

    Lucas numbers have L 1 = 1, L 2 = 3, and L n = L n−1 + L n−2. Primefree sequences use the Fibonacci recursion with other starting points to generate sequences in which all numbers are composite. Letting a number be a linear function (other than the sum) of the 2 preceding numbers. The Pell numbers have P n = 2P n−1 + P n−2.

  6. Lazy caterer's sequence - Wikipedia

    en.wikipedia.org/wiki/Lazy_caterer's_sequence

    Simply put, each number equals a triangular number plus 1. These are the first number on each row of Floyd's triangle. The lazy caterer's sequence (green) and other OEIS sequences in Bernoulli's triangle. As the third column of Bernoulli's triangle (k = 2) is a triangular number plus one, it forms the lazy caterer's sequence for n cuts, where n ...

  7. Music Review: In a new expanded collection, how much of John ...

    www.aol.com/entertainment/music-review-expanded...

    The new remixed and expanded “Mind Games: The Ultimate Collection" is for those John Lennon fans who really, really love his inconsistent 1973 record of the same name. The problem is, many ...

  8. Caleb Williams runs for TD, leads 2 scoring drives as Bears ...

    www.aol.com/caleb-williams-runs-td-leads...

    ANDREW SELIGMAN. August 17, 2024 at 4:01 PM. CHICAGO (AP) — Caleb Williams made another good impression in his first appearance at Soldier Field since Chicago drafted him with the No. 1 overall ...

  9. Repeating decimal - Wikipedia

    en.wikipedia.org/wiki/Repeating_decimal

    For example, in duodecimal, ⁠ 1 / 2 ⁠ = 0.6, ⁠ 1 / 3 ⁠ = 0.4, ⁠ 1 / 4 ⁠ = 0.3 and ⁠ 1 / 6 ⁠ = 0.2 all terminate; ⁠ 1 / 5 ⁠ = 0. 2497 repeats with period length 4, in contrast with the equivalent decimal expansion of 0.2; ⁠ 1 / 7 ⁠ = 0. 186A35 has period 6 in duodecimal, just as it does in decimal. If b is an integer base ...