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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. It was developed by the Russian engineer Jakow Trachtenberg in order to keep his mind occupied while being in a Nazi concentration camp .
The year 2000 problem[ 1], or simply Y2K, comprises potential computer errors related to the formatting and storage of calendar data for dates in and after the year 2000. Many programs represented four-digit years with only the final two digits, making the year 2000 indistinguishable from 1900. Computer systems' inability to distinguish dates ...
Frequency of first significant digit of physical constants plotted against Benford's law. Benford's law, also known as the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation that in many real-life sets of numerical data, the leading digit is likely to be small. [ 1]
Long division. In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit Hindu-Arabic numerals ( positional notation) that is simple enough to perform by hand. It breaks down a division problem into a series of easier steps. As in all division problems, one number, called the dividend, is divided by another ...
To easily multiply any 2-digit numbers together a simple algorithm is as follows (where a is the tens digit of the first number, b is the ones digit of the first number, c is the tens digit of the second number and d is the ones digit of the second number): (+) (+)
The Karatsuba algorithm is a fast multiplication algorithm. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. [ 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 ...
where the product is over all primes p, and γ c,p (n) is the number of solutions to the equation n = q 1 + ⋯ + q c mod p in modular arithmetic, subject to the constraints q 1, …, q c ≠ 0 mod p. This formula has been rigorously proven to be asymptotically valid for c ≥ 3 from the work of Ivan Matveevich Vinogradov, but is still only a ...
Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...