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Waring's Problem for Powers of Primes II


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1 Government College, Hoshiarpur, India
     

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In a recent paper, Pillai has examined one of my conjectures and proved the

THEOREM. If l ≤r ≤ 2n-2l-2 and n ≥ 20, then every integer not exceeding N is the sum of at most I nth powers of primes ≥ 1,

where

N = c(1.6)n/6.31n,

3n = 1.2r+r,

and

I = 2n+l-2.

He has not stated how far his theorem holds for values of n < 20. The object of the present paper is to study the validity of Pillai's theorem when n ≤ 19.


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  • Waring's Problem for Powers of Primes II

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Authors

Hans Raj Gupta
Government College, Hoshiarpur, India

Abstract


In a recent paper, Pillai has examined one of my conjectures and proved the

THEOREM. If l ≤r ≤ 2n-2l-2 and n ≥ 20, then every integer not exceeding N is the sum of at most I nth powers of primes ≥ 1,

where

N = c(1.6)n/6.31n,

3n = 1.2r+r,

and

I = 2n+l-2.

He has not stated how far his theorem holds for values of n < 20. The object of the present paper is to study the validity of Pillai's theorem when n ≤ 19.