Abstract
A smooth number is a number with only small prime factors. In particular, a positive integer is y-smooth if it has no prime factor exceeding y. Smooth numbers are a useful tool in number theory because they not only have a simple multiplicative structure, but are also fairly numerous. These twin properties of smooth numbers are the main reason they play a key role in almost every moder integer factorization algorithm. Smooth numbers play a similar essential role in discrete logarithm algorithms (methods to represent some group element as a power of another), and a lesser, but still important, role in primality tests.
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© 1995 Birkhäser Verlag, Basel, Switzerland
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Pomerance, C. (1995). The Role of Smooth Numbers in Number Theoretic Algorithms. In: Chatterji, S.D. (eds) Proceedings of the International Congress of Mathematicians. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-9078-6_34
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DOI: https://doi.org/10.1007/978-3-0348-9078-6_34
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