Geodesic
Small Sets of k-th Powers
Canadian mathematical bulletin, Tome 37 (1994) no. 2, pp. 168-173

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DOI

Let k ≥ 2 and q = g(k) — G(k), where g(k) is the smallest possible value of r such that every natural number is the sum of at most r k-th powers and G(k) is the minimal value of r such that every sufficiently large integer is the sum of r k-th powers. For each positive integer r ≥ q, let Then for every ε > 0 and N ≥ N(r, ε), we construct a set A of k-th powers such that |A| ≤ (r(2 + ε)r + l)N 1/(k+r) and every nonnegative integer n ≤ N is the sum of k-th powers in A. Some related results are also obtained.
DOI : 10.4153/CMB-1994-025-1
Mots-clés : 11P05 
Ding, Ping; Freedman, A. R. Small Sets of k-th Powers. Canadian mathematical bulletin, Tome 37 (1994) no. 2, pp. 168-173. doi: 10.4153/CMB-1994-025-1
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     title = {Small {Sets} of k-th {Powers}},
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     year = {1994},
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     number = {2},
     doi = {10.4153/CMB-1994-025-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-025-1/}
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