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The Arithmetic Properties Of Cyclotomic Polynomial

Posted on:2015-02-27Degree:MasterType:Thesis
Country:ChinaCandidate:Y ZhouFull Text:PDF
GTID:2250330431469616Subject:Basic mathematics
Abstract/Summary:
The n-th cyclotomic polynomial is the monic polynomial whose roots are the primitive n-th roots of unity. That is where φ(n) is the Euler totient function. Let A(n) be the largest absolute value of the coefficients of n-th cyclotomic polynomial Φn(x).Let7≤p<g<r be odd primes such that q=kp+1and4r≡1(mod pq), where k is a positive integer. If p=1(mod4) and κ>4or p≡1(mod4) and κ>2, then a(pqr,pqr-5gr+q+r+1)=2.Next, let denote the n-th cyclotomic polynomial and φ(n) is the Euler totient function. Let3<q<r be primes, then we establish property of all coefficients of Ψ3qr(x).
Keywords/Search Tags:Cyclotomic polynomial, Inverse Cyclotomic polynomial, Ternarycyclotomic polynomial
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