Borwein and Choi conjectured that a polynomial P（x） with coefficients ±1 of degree N - 1 is cyclotomic iffP（x）=±Φp1（±x）ΦP2（±x^p1）…Φpr（±x^p1p2…pr-1）,where N = P1P2 … pτ and the...Borwein and Choi conjectured that a polynomial P（x） with coefficients ±1 of degree N - 1 is cyclotomic iffP（x）=±Φp1（±x）ΦP2（±x^p1）…Φpr（±x^p1p2…pr-1）,where N = P1P2 … pτ and the pi are primes, not necessarily distinct. Here Φ（x） ：= （x^p - 1）/（x - 1） is the p-th cyclotomic polynomial. They also proved the conjecture for N odd or a power of 2. In this paper we introduce a so-called E-transformation, by which we prove the conjecture for a wider variety of cases and present the key as well as a new approach to investigate the coniecture.展开更多
基金Research partially supported by Program for New Century Excellent Talents in University Grant # NCET-06-0785by SRF for ROCS, SEM
文摘Borwein and Choi conjectured that a polynomial P（x） with coefficients ±1 of degree N - 1 is cyclotomic iffP（x）=±Φp1（±x）ΦP2（±x^p1）…Φpr（±x^p1p2…pr-1）,where N = P1P2 … pτ and the pi are primes, not necessarily distinct. Here Φ（x） ：= （x^p - 1）/（x - 1） is the p-th cyclotomic polynomial. They also proved the conjecture for N odd or a power of 2. In this paper we introduce a so-called E-transformation, by which we prove the conjecture for a wider variety of cases and present the key as well as a new approach to investigate the coniecture.
