Deshouillers, J.-M.; Dress, F. Numerical results for sums of five and seven biquadrates and consequences for sums of 19 biquadrates. (English) Zbl 0879.11052 Math. Comput. 61, No. 203, 195-207 (1993). Summary: The authors describe the algorithms which allowed them to show that all the integers congruent to 50 modulo 80 that lie in the interval \((0.3651 \times 10^{12}\), \(1.0400 \times 10^{12})\) are sums of five biquadrates, and that all the integers congruent to 67 modulo 80 that lie in the interval \((0.3651 \times 10^{12}\), \(9.5956\times 10^{18})\) are sums of seven biquadrates. They also describe some ascent lemmas used to deduce from the previous results that every integer not exceeding \(10^{448}\) is a sum of nineteen biquadrates. Cited in 1 ReviewCited in 3 Documents MSC: 11P05 Waring’s problem and variants 11-04 Software, source code, etc. for problems pertaining to number theory 11Y16 Number-theoretic algorithms; complexity Keywords:algorithms; sums of five biquadrates; sums of seven biquadrates; sum of nineteen biquadrates × Cite Format Result Cite Review PDF Full Text: DOI