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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. Trachtenberg system - Wikipedia

    en.wikipedia.org/wiki/Trachtenberg_system

    The Trachtenberg system is a system of rapid mental calculation.The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly.

  4. Casting out nines - Wikipedia

    en.wikipedia.org/wiki/Casting_out_nines

    Since we are adding 1 to the tens digit and subtracting one from the units digit, the sum of the digits should remain the same. For example, 9 + 2 = 11 with 1 + 1 = 2. When adding 9 to itself, we would thus expect the sum of the digits to be 9 as follows: 9 + 9 = 18, (1 + 8 = 9) and 9 + 9 + 9 = 27, (2 + 7 = 9).

  5. Multiplication - Wikipedia

    en.wikipedia.org/wiki/Multiplication

    Area of a cloth 4.5m × 2.5m = 11.25m 2; 4 ⁠ 1 / 2 ⁠ × 2 ⁠ 1 / 2 ⁠ = 11 ⁠ 1 / 4 ⁠ Multiplication (often denoted by the cross symbol × , by the mid-line dot operator ⋅ , by juxtaposition, or, on computers, by an asterisk * ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition ...

  6. How to Solve It - Wikipedia

    en.wikipedia.org/wiki/How_to_Solve_It

    How to Solve It (1945) is a small volume by mathematician George Pólya, describing methods of problem solving. [ 1 ] This book has remained in print continually since 1945.

  7. Equation solving - Wikipedia

    en.wikipedia.org/wiki/Equation_solving

    For example, the equation x + y = 2x – 1 is solved for the unknown x by the expression x = y + 1, because substituting y + 1 for x in the equation results in (y + 1) + y = 2(y + 1) – 1, a true statement. It is also possible to take the variable y to be the unknown, and then the equation is solved by y = x – 1.

  8. Millennium Prize Problems - Wikipedia

    en.wikipedia.org/wiki/Millennium_Prize_Problems

    The real part of every nontrivial zero of the Riemann zeta function is 1/2. The Riemann hypothesis is that all nontrivial zeros of the analytical continuation of the Riemann zeta function have a real part of ⁠ 1 / 2 ⁠. A proof or disproof of this would have far-reaching implications in number theory, especially for the distribution of prime ...

  9. Algebraic operation - Wikipedia

    en.wikipedia.org/wiki/Algebraic_operation

    [8] [9] In programming languages such as Ada, [10] Fortran, [11] Perl, [12] Python [13] and Ruby, [14] a double asterisk is used, so x 2 is written as x ** 2. The plus–minus sign , ±, is used as a shorthand notation for two expressions written as one, representing one expression with a plus sign, the other with a minus sign.