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Waring's Problem for Powers of Primes II
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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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