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| A Note on the Completeness of an Exponential Type Sequence |
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Citation： |
Jinhui FANG.A Note on the Completeness of an Exponential Type Sequence[J].Chinese Annals of Mathematics B,2011,32(4):527~532 |
| Page view： 1812
Net amount： 1242 |
Authors： |
Jinhui FANG; |
Foundation： |
the National Natural Science Foundation of China (Nos. 10771103, 11071121). |
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| Abstract： |
For any given coprime integers p and q greater than 1, in 1959, B. J. Birch
proved that all sufficiently large integers can be expressed as a sum of pairwise distinct
terms of the form paqb. As Davenport observed, Birch’s proof can be modified to show
that the exponent b can be bounded in terms of p and q. In 2000, N. Hegyvari gave an
effective version of this bound. The author improves this bound. |
Keywords： |
Complete sequence, Coprime, Residue |
Classification： |
11A07, 11B13 |
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