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 rest of this article presents some methods devised by Trachtenberg. Some of the algorithms Trachtenberg developed are ones for general multiplication, division and addition. Also, the Trachtenberg system includes some specialised methods for multiplying small numbers between 5 and 13 (but shown here is 2–12).
The section on addition demonstrates an effective method of checking calculations that can also be applied to multiplication.
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The Trachtenbergsystem is a system of rapid mental calculation. The system consists of a number of readily memorized operations that allow one to perform...
Look up trachtenberg in Wiktionary, the free dictionary. Trachtenberg (Russian/Ukrainian: Трахтенберг, Yiddish: טראַכֿטנבערג; Hebrew: טרכטנברג, is a surname...
Jakow Trachtenberg (17 June 1888 – 26 October 1951) was a mathematician who developed the mental calculation techniques called the Trachtenbergsystem. He...
relation (LLL; KZ) Modular exponentiation Montgomery reduction Schoof Trachtenbergsystem Italics indicate that algorithm is for numbers of special forms...
relation (LLL; KZ) Modular exponentiation Montgomery reduction Schoof Trachtenbergsystem Italics indicate that algorithm is for numbers of special forms...
recorded habit of experimentation with numbers. Similar systems include the Trachtenbergsystem or the techniques mentioned in Lester Meyers's 1947 book...
difficulty of both problems has been used to construct various cryptographic systems. There exist groups for which computing discrete logarithms is apparently...
ideal as {a, b}. This convention is followed by many computer algebra systems. Nonetheless, some authors leave gcd(0, 0) undefined. The GCD of a and...
Number-theoretic transform Prosthaphaeresis Slide rule Trachtenbergsystem Residue number system § Multiplication for another fast multiplication algorithm...
relation (LLL; KZ) Modular exponentiation Montgomery reduction Schoof Trachtenbergsystem Italics indicate that algorithm is for numbers of special forms...
relation (LLL; KZ) Modular exponentiation Montgomery reduction Schoof Trachtenbergsystem Italics indicate that algorithm is for numbers of special forms...
relation (LLL; KZ) Modular exponentiation Montgomery reduction Schoof Trachtenbergsystem Italics indicate that algorithm is for numbers of special forms...
relation (LLL; KZ) Modular exponentiation Montgomery reduction Schoof Trachtenbergsystem Italics indicate that algorithm is for numbers of special forms...
publicly known method in a useful time period on any available computer system or computer cluster such as supercomputers and computer grids. The largest...
relation (LLL; KZ) Modular exponentiation Montgomery reduction Schoof Trachtenbergsystem Italics indicate that algorithm is for numbers of special forms...
fraction Egyptian mathematics Multiplication algorithms Binary numeral system Neugebauer, Otto (1969) [1957]. The Exact Sciences in Antiquity (2 ed.)...
step unnecessary. See Methods of computing square roots § Binary numeral system (base 2) for an example. Some programming languages dedicate an explicit...
relation (LLL; KZ) Modular exponentiation Montgomery reduction Schoof Trachtenbergsystem Italics indicate that algorithm is for numbers of special forms...
"Riemann's Hypothesis and Tests for Primality". Journal of Computer and System Sciences. 13 (3): 300–317. doi:10.1016/S0022-0000(76)80043-8. Agrawal, Manindra;...
relation (LLL; KZ) Modular exponentiation Montgomery reduction Schoof Trachtenbergsystem Italics indicate that algorithm is for numbers of special forms...
relation (LLL; KZ) Modular exponentiation Montgomery reduction Schoof Trachtenbergsystem Italics indicate that algorithm is for numbers of special forms...
and explicit aspects of the Langlands program. Magma computer algebra system SageMath Number Theory Library PARI/GP Fast Library for Number Theory Eric...
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