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Rough number

From Wikipedia, the free encyclopedia

Ak-rough number,as defined by Finch in 2001 and 2003, is a positiveintegerwhoseprime factorsare all greater than or equal tok.k-roughness has alternately been defined as requiring all prime factors to strictly exceedk.[1]

Examples (after Finch)

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  1. Every odd positive integer is 3-rough.
  2. Every positive integer that iscongruentto 1 or 5 mod 6 is 5-rough.
  3. Every positive integer is 2-rough, since all its prime factors, being prime numbers, exceed 1.

See also

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Notes

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  1. ^p. 130, Naccache and Shparlinski 2009.

References

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  • Weisstein, Eric W."Rough Number".MathWorld.
  • Finch's definition from Number Theory Archives
  • "Divisibility, Smoothness and Cryptographic Applications", D. Naccache and I. E. Shparlinski, pp. 115–173 inAlgebraic Aspects of Digital Communications,eds. Tanush Shaska and Engjell Hasimaj, IOS Press, 2009,ISBN9781607500193.

TheOn-Line Encyclopedia of Integer Sequences(OEIS) listsp-rough numbers for smallp: