Covers of the integers with odd moduli and their applications to the forms xm-2n and x2-F3n/2

@article{Wu2009CoversOT,
  title={Covers of the integers with odd moduli and their applications to the forms xm-2n and x2-F3n/2},
  author={Ke-Jian Wu and Zhi-Wei Sun},
  journal={Math. Comput.},
  year={2009},
  volume={78},
  pages={1853-1866}
}
  • Ke-Jian Wu, Zhi-Wei Sun
  • Published in Math. Comput. 2009
  • Mathematics, Computer Science
  • In this paper we construct a cover {a s (mod n s )} k s=1 of ℤ with odd moduli such that there are distinct primes p 1 ,...,p k dividing 2 n1 ―1,..., nk ― 1 respectively. Using this cover we show that for any positive integer m divisible by none of 3, 5, 7, 11, 13 there exists an infinite arithmetic progression of positive odd integers the mth powers of whose terms are never of the form 2 n ± p a with a, n ∈ {0,1,2,...} and p a prime. We also construct another cover of Z with odd moduli and use… CONTINUE READING

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