On integers not of the form ±𝑝^{𝑎}±𝑞^{𝑏}

Sun, Zhi-Wei

doi:10.1090/S0002-9939-99-05502-1

On integers not of the form $\pm p^a\pm q^b$
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by Zhi-Wei Sun

Proc. Amer. Math. Soc. 128 (2000), 997-1002

DOI: https://doi.org/10.1090/S0002-9939-99-05502-1

Published electronically: October 27, 1999

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Abstract:

In 1975 F. Cohen and J.L. Selfridge found a 94-digit positive integer which cannot be written as the sum or difference of two prime powers. Following their basic construction and introducing a new method to avoid a bunch of extra congruences, we are able to prove that if \begin{equation*} \hspace {-1.5pc} x\equiv 47867742232066880047611079 (\operatorname {mod} 66483034025018711639862527490), \hspace {-1.5pc} \end{equation*} then $x$ is not of the form $\pm p^{a}\pm q^{b}$ where $p,q$ are primes and $a,b$ are nonnegative integers.

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