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On Waring's Problem IX


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1 Annamalainagar, India
     

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Vinogradow has proved not only the amazing result that every large number is the sum of a finite number of nth powers of primes, but has also found out a formula for its upper bound. Let g1(n) denote the least value of s such that every number from the beginning is the sum of s nth powers of primes or unity. Then it is likely that when n > n0

g1(n)=2n+l-2,

where l=[(3/2)n].

The object of this paper is to prepare the way for it.


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  • On Waring's Problem IX

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Authors

S. S. Pillai
Annamalainagar, India

Abstract


Vinogradow has proved not only the amazing result that every large number is the sum of a finite number of nth powers of primes, but has also found out a formula for its upper bound. Let g1(n) denote the least value of s such that every number from the beginning is the sum of s nth powers of primes or unity. Then it is likely that when n > n0

g1(n)=2n+l-2,

where l=[(3/2)n].

The object of this paper is to prepare the way for it.