Abstract
Let
k
be an integer greater than 2. We consider the problem of constructing as many (different) numbers as possible that are sums of s positive integral kth powers. One construction has been given by Hardy and Little wood (1925) in their work on Waring’s Problem. It consists of taking all numbers of the form m
k
+ m', 0 < m' < (m + 1)
k
—
m
k
where
m
' runs through numbers that are representable as the sum of
s
— 1
k
th powers.
Cited by
4 articles.
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1. The use in additive number theory of numbers without large prime factors;Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences;1993-11-15
2. Waring's problem for polynomials of small degree;Mathematical Notes of the Academy of Sciences of the USSR;1985-09
3. Pairs of additive equations IV. Sextic equations;Acta Arithmetica;1984
4. Pairs of additive equations III: quintic equations;Proceedings of the Edinburgh Mathematical Society;1983-06