AIMS Mathematics, 2019, 4(1): 79-85. doi: 10.3934/Math.2019.1.79

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On the gap between prime ideals

Mathematical College, Sichuan University, Chengdu 610064, China

We define a gap function to measure the difference of two distinct prime ideals in a given number field. In this paper, we determine all quadratic fields and cyclotomic fields satisfying the condition: There exist two distinct prime ideals whose gap is 1.
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4. T. Metsänkylä, Catalan's conjecture: Another old Diophantine problem solved, B. Am. Math. Soc., 41 (2004), 43-57.

© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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