On integers of the form 2^{π}Β±π^{πΌβ}βπ^{πΌβ}ββ¦π^{πΌα΅£}α΅£
Yong-Gao Chen Β· Proceedings of the American Mathematical Society Β· 1999
In this paper we prove that the set of positive odd integers which have no representation of the form 2 n Β± p Ξ± q Ξ² 2^{n} \pm p^{\alpha } q^{\beta } , where p p , q q are distinct odd primes and n , Ξ± , Ξ² n, \alpha ,\beta are nonnegative integers, has positive lower asymptotic density in the set of all positive odd integers.