Covers of the integers with odd moduli and their applications to the forms $x^m-2^n$ and $x^2-F_{3n}/2$

Ke-Jian Wu, Zhi-Wei Sun

In this paper we construct a cover {a_s(mod n_s)}_{s=1}^k of Z with odd moduli such that there are distinct primes p_1,...,p_k dividing 2^{n_1}-1,...,2^{n_k}-1 respectively. Using…