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  2. Karatsuba algorithm - Wikipedia

    en.wikipedia.org/wiki/Karatsuba_algorithm

    [1] [2] [3] It is a divide-and-conquer algorithm that reduces the multiplication of two n-digit numbers to three multiplications of n/2-digit numbers and, by repeating this reduction, to at most ⁡ single-digit multiplications.

  3. Trachtenberg system - Wikipedia

    en.wikipedia.org/wiki/Trachtenberg_system

    If the answer is greater than a single digit, simply carry over the extra digit (which will be a 1 or 2) to the next operation. The remaining digit is one digit of the final result. Example: Determine neighbors in the multiplicand 0316: digit 6 has no right neighbor; digit 1 has neighbor 6; digit 3 has neighbor 1

  4. 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 ...

  5. Multiplication algorithm - Wikipedia

    en.wikipedia.org/wiki/Multiplication_algorithm

    To multiply two numbers with n digits using this method, one needs about n 2 operations. More formally, multiplying two n-digit numbers using long multiplication requires Θ(n 2) single-digit operations (additions and multiplications).

  6. Computational complexity of mathematical operations - Wikipedia

    en.wikipedia.org/wiki/Computational_complexity...

    Operation Input Output Algorithm Complexity Addition: Two -digit numbers : One +-digit number : Schoolbook addition with carry ()Subtraction: Two -digit numbers : One +-digit number

  7. Promptuary - Wikipedia

    en.wikipedia.org/wiki/Promptuary

    The next band from the right has three digits, 2, 1 and 8. These are added together to get 11. The units digit of this addition, 1, is written down as the next digit of the multiplication result. The tens digit, which is 1, is carried into the next band. The third band from the right has five digits, 2, 4, 3, 1 and 6 plus the carried 1.

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  9. Transposable integer - Wikipedia

    en.wikipedia.org/wiki/Transposable_integer

    The integer X is the repeating digits of the fraction 1 ⁄ F, say d p d p-1...d 3 d 2 d 1, where d p, d p-1, ..., d 3, d 2 and d 1 each represents a digit and p is the number of digits. The multiple n X is thus the repeating digits of the fraction n ⁄ F, say d k d k-1...d 3 d 2 d 1 d p d p-1...d k+2 d k+1, representing the results after ...

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