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On the easier Waring problem for powers of primes. I

Published online by Cambridge University Press:  24 October 2008

Paul Erdös
Paul Erdös
Affiliation:
[Dedicated to Prof. E. Landau on his 60th birthday]
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Extract

The famous theorem of Schnirelmann states that a constant c exists such that every integer greater than one may be expressed as the sum of at most c primes. Recently, Heilbronn, Landau and Scherk proved that this holds with c = 71. Probably the true value of c is 3. Another well-known theorem (Hilbert's solution of Waring's problem) is that every integer is the sum of a bounded number of positive kth powers. If we omit the restriction that all the kth powers are positive, the problem is referred to as the easier Waring problem and the proof of the result is then much simpler.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 33 , Issue 1 , March 1937 , pp. 6 - 12
Copyright
Copyright © Cambridge Philosophical Society 1937

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References

* “Le crible d'Eratosthène et le théorème de Goldbach”, Videnskapsselskapets Skrifter, I, Mat. Naturv. Klasse 1920,Google Scholar No. 3, Kristiania.

† Loc. cit. p. 22, eqn. (20).

‡ ‘Über additive Eigenschaften von Zahlen”, Math. Annalen, 107 (1933), 649–690, p. 670.Google Scholar Lemma 3 can be deduced from Lemma 2.