Abstract
Let \({a \geqq 2}\) be an even integer and let \({L \geqq 1}\) be an integer. We show that for a sufficiently large x, the number of primes \({p \leqq x}\) such that 2p + 2a, . . . , 2p + 2La can not be expressed as \({a^{k} +\phi(m)}\) is at least \({C(a,L) \frac{x}{log x}}\), where k, m are positive integers, \({\phi(m)}\) is the Euler totient function and the constant C(a, L) depends on a, L.
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Supported by the National Natural Science Foundation of China (11471017) and the Natural Science Foundation of HuaiHai Institute of Technology (KQ10002).
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Sun, XG. On integers 2(p + ia) not of the form \({a^k + \phi(m)}\) . Acta Math. Hungar. 146, 332–340 (2015). https://doi.org/10.1007/s10474-015-0524-7
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DOI: https://doi.org/10.1007/s10474-015-0524-7