Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. W. S. Cassels, Über Basen der natürlichen Zahlenreihe, Abh. Math. Sem. Univ. Hamburg. 21 (1957), 247–257.
L. Chatrovsky, Sur les bases minimales de la suite des nombres naturels (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 4 (1940), 335–340.
P. Erdős and M. B. Nathanson, Oscillations of bases for the natural numbers, Proc. Amer. Math. Soc. 53 (1957), 253–258.
P. Erdős and M. B. Nathanson, Systems of distinct representatives and minimal bases in additive number theory, in: M. B. Nathanson (ed.), Number Theory, Carbondale 1979, Lecture Notes in Mathematics, vol. 751, Springer-Verlag, Heidelberg, 1979, pp. 89–107.
P. Erdős and M. B. Nathanson, Minimal asymptotic bases for the natural numbers, J. Number Theory 12 (1980), 154–159.
P. Erdős and M. B. Nathanson, Lagrange's theorem and thin subsequences of squares, in: J. Gani and V. K. Rohatgi (eds.), Contributions to Probability, Academic Press, New York, 1981, pp. 3–9.
P. Erdős and M. B. Nathanson, Independence of solution sets in additive number theory, in: G.-C. Rota (ed.), Probability, Statistical Mechanics, and Number Theory, Academic Press, 1986, pp. 97–105.
P. Erdős and A. Renyi, Additive properties of random sequences of positive integers, Acta Arith. 6 (1960), 83–110.
P. Erdős and P. Turán, On a problem of Sidon in additive number theory, and some related problems, J. London Math. Soc. 16 (1941), 212–215; Addendum (by P. Erdős) ibid. 19 (1944), 208.
E. Härtter, Ein Beitrag zur Theorie der Minimalbasen, J. Reine Angew. Math. 196 (1956), 170–204.
M. B. Nathanson, Minimal bases and maximal nonbases in additive number theory, J. Number Theory 6 (1974), 324–333.
M. B. Nathanson, Waring's problem for sets of density zero, in: M. I. Knopp (ed.), Number Theory, Philadelphia 1980, Lecture Notes in Mathematics, vol. 899, Springer-Verlag, Heidelberg, 1981, pp. 301–310.
D. Raikov, Über die Basen der natürlichen Zahlenreihe, Mat. Sbor. N.S. 2 (44) (1937), 595–597.
L. G. Shnirel'man, Über additive Eigenschaften von Zahlen, Math. Ann. 107 (1933), 649–690.
A. Stöhr, Eine Basis h-ter Ordnung für die Menge aller natürlichen Zahlen, Math. Zeit. 42 (1937), 739–743.
A. Stöhr, Gelöste und ungelöste Fragen über Basen der natürlichen Zahlenreihe I,II, J. Reine Angew. Math. 194 (1955), 40–65, 111–140.
J. Zöllner, Der Vier-Quadrate-Satz und ein Problem von Erdős und Nathanson, Dissertation, Johannes Gutenberg-Universität, Mainz, 1984.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1987 Springer-Verlag
About this paper
Cite this paper
Erdős, P., Nathanson, M.B. (1987). Problems and results on minimal bases in additive number theory. In: Chudnovsky, D.V., Chudnovsky, G.V., Cohn, H., Nathanson, M.B. (eds) Number Theory. Lecture Notes in Mathematics, vol 1240. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072974
Download citation
DOI: https://doi.org/10.1007/BFb0072974
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17669-5
Online ISBN: 978-3-540-47756-3
eBook Packages: Springer Book Archive