Some questions of Erdős and Graham on numbers of the form

Authors:
Peter Borwein and Terry A. Loring

Journal:
Math. Comp. **54** (1990), 377-394

MSC:
Primary 11A63; Secondary 11-04, 11D68, 11K16

MathSciNet review:
990598

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Abstract | References | Similar Articles | Additional Information

Abstract: Erdös in 1975 and Erdös and Graham in 1980 raised several questions concerning representing numbers as series of the form . For example, does the equation

*n*? The answer to this question is affirmative; in fact, we conjecture that the above equation is solvable for every

*n*. This conjecture is based on a more general conjecture, namely that the algorithm

**[1]**P. Erdős,*Some problems and results on the irrationality of the sum of infinite series*, J. Math. Sci.**10**(1975), 1–7 (1976). MR**539489****[2]**-,*Sur l'irrationalité d'une certaine série*, C. R. Acad. Sci. Paris Ser. I Math.**292**(1981), 65-768.**[3]**P. Erdös and R. L. Graham,*Old and new results in combinatorial number theory*, Monograph No. 28 de d'Enseignement Mathématique, Genève, 1980.**[4]**Donald E. Knuth,*The art of computer programming. Vol. 2*, 2nd ed., Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms; Addison-Wesley Series in Computer Science and Information Processing. MR**633878****[5]**Jeffrey C. Lagarias,*The 3𝑥+1 problem and its generalizations*, Amer. Math. Monthly**92**(1985), no. 1, 3–23. MR**777565**, 10.2307/2322189

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DOI:
http://dx.doi.org/10.1090/S0025-5718-1990-0990598-9

Article copyright:
© Copyright 1990
American Mathematical Society