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A k-rough number, as defined by Finch in 2001 and 2003, is a positive integer whose prime factors are all greater than or equal to k. k-roughness has alternately been defined as requiring all prime factors to strictly exceed k.[1]
Examples (after Finch)
Every odd positive integer is 3-rough.
Every positive integer that is congruent to 1 or 5 mod 6 is 5-rough.
Every positive integer is 2-rough, since all its prime factors, being prime numbers, exceed 1.
"Divisibility, Smoothness and Cryptographic Applications", D. Naccache and I. E. Shparlinski, pp. 115–173 in Algebraic Aspects of Digital Communications, eds. Tanush Shaska and Engjell Hasimaj, IOS Press, 2009, ISBN9781607500193.
This page was last edited on 31 October 2023, at 15:10