Waring's problem for sixteen biquadrates. Numerical results
Journal de théorie des nombres de Bordeaux, Tome 12 (2000) no. 2, pp. 411-422.

Nous expliquons les algorithmes qui nous ont permis de vérifier que tout entier congru à 4 modulo 80 dans l’intervalle [6×10 12 ;2.17×10 14 ] est la somme de 5 bicarrés, et que tout entier congru à 6,21 ou 36 modulo 80 dans l’intervalle [6×10 12 ;1.36×10 23 ] est la somme de 7 bicarrés. Nous indiquons également des résultats déduits de calculs portant sur les petites sommes de bicarrés. L’escalade de Dickson appliquée à ces résultats montre que tout entier de l’intervalle [13793;10 245 ] est la somme de 16 bicarrés.

We explain the algorithms that we have implemented to show that all integers congruent to 4 modulo 80 in the interval [6×10 12 ;2.17×10 14 ] are sums of five fourth powers, and that all integers congruent to 6,21 or 36 modulo 80 in the interval [6×10 12 ;1.36×10 23 ] are sums of seven fourth powers. We also give some results related to small sums of biquadrates. Combining with the Dickson ascent method, we deduce that all integers in the interval [13793;10 245 ] are sums of 16 biquadrates.

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     title = {Waring's problem for sixteen biquadrates. {Numerical} results},
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Deshouillers, Jean-Marc; Hennecart, François; Landreau, Bernard. Waring's problem for sixteen biquadrates. Numerical results. Journal de théorie des nombres de Bordeaux, Tome 12 (2000) no. 2, pp. 411-422. http://www.numdam.org/item/JTNB_2000__12_2_411_0/

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