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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1993-1201766-8
PII: S 0025-5718(1993)1201766-8
Article copyright: © Copyright 1993 American Mathematical Society