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Estimates of the least prime factor of a binomial coefficient
Author(s) -
Konyagin S. V.
Publication year - 1999
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300007555
Subject(s) - mathematics , binomial coefficient , integer (computer science) , prime factor , prime (order theory) , constant (computer programming) , combinatorics , negative binomial distribution , function (biology) , discrete mathematics , statistics , poisson distribution , evolutionary biology , computer science , biology , programming language
Let k be a positive integer and g ( k ) be the least integer n > k + 1 such that all prime factors of(k n )are > k . We prove that g ( k ) ⩾ exp ( c log 2 k ) ,where c is an absolute positive constant. We also establish a new theorem on the distribution of fractional parts of a smooth function.