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Mathematics of Computation

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Not every number is the sum or difference of two prime powers

Authors: Fred Cohen and J. L. Selfridge
Journal: Math. Comp. 29 (1975), 79-81
MSC: Primary 10J15; Secondary 10-04
MathSciNet review: 0376583
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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 [Enhancements On Off] (What's this?)

  • [1] P. ERDÖS, "On integers of the form $ {2^k} + p$ and some related problems," Summa Brasil. Math., v. 2, 1950, pp. 113-123. MR 13, 437. MR 0044558 (13:437i)

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Article copyright: © Copyright 1975 American Mathematical Society

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