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References [1] Apostol , T. M. 1976 Introduction to Analytic Number Theory Springer New York

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. Smyth , C. J. 2001 On the metric Mahler measure J. Number Theory 86 368 – 387 10.1006/jnth.2000.2579 . [4

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Tachiya , Y. , Irrationality of Lambert series associated with a periodic sequence , Int. J. Number Theory 10 ( 2014 ), 623 – 636 . [12] Matala

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J. Number Theory 4 516 – 528 10.1016/0022-314X(79)90031-3 . [7] Gallagher , P. X. 1970 A large sieve density estimate near

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] G aal , I. and R emete , L. , Integral bases and monogenity of pure fields , Journal of Number Theory , 173 ( 2017 ), 129 – 146 . [6] G aál , I. and R emete

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Tsukuba J. Math. 17 443 453 MONTGOMERY, H. L., Topics in multiplicative number theory , Lecture Notes in

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. Ubis , A. 2007 Visible points in the sphere J. Number Theory 126 200 – 211 10.1016/j.jnt.2006.11.010 . [3

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] Chen , J. H. , Voutier , P. 1997 Complete solution of the Diophantine equation X 2 +1= dY 4 and a related family of quartic Thue equations J. Number Theory 62 71 – 99 10.1006/jnth.1997.2018 . [7

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1961 8 83 86 Guy, R. K. , Unsolved problem in number theory , Springer-Verlag (New York, 1994

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Convexity and the beta invariant Discrete Comput Geom. 22 411 424 Balog, A. and Deshouillers, J-M., On some convex lattice polytopes, in: Number theory in progress, Volume 2: Elementary and analytic number theory (K. Györy et al

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