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A congruence relation of the Catalan-Mersenne numbers

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Abstract

The Catalan-Mersenne numbers cn are double Mersenne numbers defined by c0 = 2 and \({c_n} = {2^{{c_{n - 1}}}} - 1\) for positive integers n. We prove a certain congruence relation of the Catalan- Mersenne numbers.

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References

  1. L. E. Dickson, History of the theory of numbers, Vol. 1: Divisibility and primality, New York, Dover (2005).

    MATH  Google Scholar 

  2. D. H. Lehmer, An extended theory of Lucas’ functions, Ann. of Math. (2), 31(3) (1930), 419–448.

    Article  MathSciNet  MATH  Google Scholar 

  3. É. Lucas, Théorie des fonctions numériques simplement périodiques, Amer. J. Math., 1 (1878), 184–240, 289–321.

    Article  MathSciNet  MATH  Google Scholar 

  4. K. H. Rosen, Elementary number theory and its applications, sixth edition, Pearson Addison Wesley (2011).

    Google Scholar 

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Correspondence to Ick Sun Eum.

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This work was supported by the Dongguk University Research Fund of 2017 and the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. NRF-2017R1C1B5017567).

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Eum, I.S. A congruence relation of the Catalan-Mersenne numbers. Indian J Pure Appl Math 49, 521–526 (2018). https://doi.org/10.1007/s13226-018-0281-8

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  • DOI: https://doi.org/10.1007/s13226-018-0281-8

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