On integers not of the form

Author:
Zhi-Wei Sun

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

MSC (2000):
Primary 11B75; Secondary 11B25, 11P32

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

Published electronically:
October 27, 1999

MathSciNet review:
1695111

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

then is not of the form where are primes and are nonnegative integers.

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Additional Information

**Zhi-Wei Sun**

Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China

Email:
zwsun@netra.nju.edu.cn

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

Received by editor(s):
June 16, 1998

Published electronically:
October 27, 1999

Additional Notes:
This research was supported by the National Natural Science Foundation of the People’s Republic of China and the Return-from-abroad Foundation of the Chinese Educational Committee

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 2000
American Mathematical Society