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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Not every number is the sum or difference of two prime powers
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by Fred Cohen and J. L. Selfridge PDF
Math. Comp. 29 (1975), 79-81 Request permission

Abstract:

Every odd number less than 262144 is the sum or difference of a power of two and a prime. An interesting example is $113921 = p - {2^{141}}$. Using covering congruences, we exhibit a 26-digit odd number which is neither the sum nor difference of a power of two and a prime. The method is then modified to exhibit an arithmetic progression of numbers which are not the sum or difference of two prime powers.
References
  • P. Erdös, On integers of the form $2^k+p$ and some related problems, Summa Brasil. Math. 2 (1950), 113–123. MR 44558
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Math. Comp. 29 (1975), 79-81
  • MSC: Primary 10J15; Secondary 10-04
  • DOI: https://doi.org/10.1090/S0025-5718-1975-0376583-0
  • MathSciNet review: 0376583