2,877 research outputs found
Non-Beiter ternary cyclotomic polynomials with an optimally large set of coefficients
Let l>=1 be an arbitrary odd integer and p,q and r primes. We show that there
exist infinitely many ternary cyclotomic polynomials \Phi_{pqr}(x) with
l^2+3l+5<= p<q<r such that the set of coefficients of each of them consists of
the p integers in the interval [-(p-l-2)/2,(p+l+2)/2]. It is known that no
larger coefficient range is possible. The Beiter conjecture states that the
cyclotomic coefficients a_{pqr}(k) of \Phi_{pqr} satisfy |a_{pqr}(k)|<= (p+1)/2
and thus the above family contradicts the Beiter conjecture. The two already
known families of ternary cyclotomic polynomials with an optimally large set of
coefficients (found by G. Bachman) satisfy the Beiter conjecture.Comment: 20 pages, 7 Table
Part-time work by high school seniors: Sorting out correlates and possible consequences (rev. ed.)
https://deepblue.lib.umich.edu/bitstream/2027.42/137892/1/occ32.pd
When four months equal a year: An exploration of inconsistencies in students' monthly versus yearly reports of drug use
https://deepblue.lib.umich.edu/bitstream/2027.42/137903/1/occ9.pd
The impacts of response styles on black-white differences in self-esteem: An analysis of six samples of youth
https://deepblue.lib.umich.edu/bitstream/2027.42/137900/1/occ16.pd
National survey results on drug use from the Monitoring the Future study, 1975-1995. Volume I: Secondary school students.
https://deepblue.lib.umich.edu/bitstream/2027.42/137816/1/mtf-vol1_1995.pd
Drug use among American high school seniors, college students and young adults, 1975-1990. Volume II: College students and young adults.
https://deepblue.lib.umich.edu/bitstream/2027.42/137830/1/mtf-vol2_1990.pd
National survey results on drug use from the Monitoring the Future study, 1975-1994. Volume II: College students and young adults.
https://deepblue.lib.umich.edu/bitstream/2027.42/137820/1/mtf-vol2_1994.pd
Correlates of drug use, part I: Selected measures of background, recent experiences, and lifestyle orientations
https://deepblue.lib.umich.edu/bitstream/2027.42/137904/1/occ8.pd
Response styles revisited: Racial/ethnic and gender differences in extreme responding
https://deepblue.lib.umich.edu/bitstream/2027.42/137850/1/occ72.pd
Student drug use, attitudes, and beliefs: National trends, 1975-1982.
https://deepblue.lib.umich.edu/bitstream/2027.42/137839/1/mtf-vol1_1982.pd
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