# 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} }

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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