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  2. Karatsuba algorithm - Wikipedia

    en.wikipedia.org/wiki/Karatsuba_algorithm

    The standard procedure for multiplication of two n-digit numbers requires a number of elementary operations proportional to , or () in big-O notation. Andrey Kolmogorov conjectured that the traditional algorithm was asymptotically optimal , meaning that any algorithm for that task would require Ω ( n 2 ) {\displaystyle \Omega (n^{2 ...

  3. 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).

  4. 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

  5. Blackstone's Card Trick Without Cards - Wikipedia

    en.wikipedia.org/wiki/Blackstone's_Card_Trick...

    The series of mathematical manipulations results in any given card producing a unique number. The multiplication by 2 and 5 means that the final number is ten times the card's value, plus a fixed 15 (for the addition of 3 and the multiplication by 5) and an additional suit-dependent figure. Thus both suit and value are readily identifiable.

  6. Schönhage–Strassen algorithm - Wikipedia

    en.wikipedia.org/wiki/Schönhage–Strassen...

    The run-time bit complexity to multiply two n-digit numbers using the algorithm is (⁡ ⁡ ⁡) in big O notation. The Schönhage–Strassen algorithm was the asymptotically fastest multiplication method known from 1971 until 2007.

  7. Divisibility rule - Wikipedia

    en.wikipedia.org/wiki/Divisibility_rule

    So add five times the last digit to the number formed by the remaining digits, and continue to do this until a number is obtained for which it is known whether it is divisible by 7. [9] Another method is multiplication by 3. A number of the form 10x + y has the same remainder when divided by 7 as 3x + y. One must multiply the leftmost digit of ...

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