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The algorithm was introduced in 1978 by the number theorist John M. Pollard, in the same paper as his better-known Pollard's rho algorithm for solving the same problem. [1] [2] Although Pollard described the application of his algorithm to the discrete logarithm problem in the multiplicative group of units modulo a prime p, it is in fact a ...
Pollard's rho algorithm for logarithms is an algorithm introduced by John Pollard in 1978 to solve the discrete logarithm problem, ... 2 2 3 20 2 1 1000 3 3 4 100 2 2 ...
Finally, in an operation too simple to really be called a fourth stage, the results of the second and third stages can be rearranged by simple algebraic manipulation to work out the desired discrete logarithm x = f 0 log g (−1) + f 1 log g 2 + f 2 log g 3 + ··· + f r log g p r − s. The first and third stages are both embarrassingly ...
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
The graph of the logarithm base 2 crosses the x-axis at x = 1 and passes through the points (2, 1), (4, 2), and (8, 3), depicting, e.g., log 2 (8) = 3 and 2 3 = 8. The graph gets arbitrarily close to the y-axis, but does not meet it. Addition, multiplication, and exponentiation are three of the most fundamental arithmetic operations.
For example, log 10 10000 = 4, and log 10 0.001 = −3. These are instances of the discrete logarithm problem. Other base-10 logarithms in the real numbers are not instances of the discrete logarithm problem, because they involve non-integer exponents. For example, the equation log 10 53 = 1.724276… means that 10 1.724276… = 53.