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Numerical results for sums of five and seven biquadrates and consequences for sums of $ 19$ biquadrates

Authors: J.-M. Deshouillers and F. Dress
Journal: Math. Comp. 61 (1993), 195-207
MSC: Primary 11P05; Secondary 11Y16
MathSciNet review: 1201766
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Abstract: We describe the algorithms which allowed us 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. We finally describe some ascent lemmas that we use to deduce from the previous results that every integer not exceeding $ {10^{448}}$ is a sum of 19 biquadrates.

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Article copyright: © Copyright 1993 American Mathematical Society