Linear congruential generator
The Lehmer algorithm can be written as
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y_{n+1}\equiv ay_n + b~~(\mod m),}
where the user chooses Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m} , and a seed value to initiate the algorithm, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y_0} .
See the prime modulus multiplicative linear congruential generator page.
References
- D. H. Lehmer, "Mathematical methods in large-scale computing units", Proceedings of the 2nd Symposium on Large-Scale Digital Calculating Machinery, vol XXVI pp. 141-146 The Annals of the Computational Laboratory of Harvard University, Harvard University Press (1951)