Enumerating solutions to 𝑝(𝑎)+𝑞(𝑏)=𝑟(𝑐)+𝑠(𝑑)

DOI10.1090/S0025-5718-00-01219-9zbMath0960.11055MaRDI QIDQ4517530

Daniel J. Bernstein

Publication date: 22 November 2000

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

algorithmEuler equationcubic Diophantine equationquartic Diophantine equationsum of two cubessums of seventh powers

Mathematics Subject Classification ID

Waring's problem and variants (11P05) Computer solution of Diophantine equations (11Y50) Cubic and quartic Diophantine equations (11D25) Higher degree equations; Fermat's equation (11D41)

Related Items (6)

Brauer groups of diagonal quartic surfaces ⋮ Unnamed Item ⋮ Bimonotone enumeration ⋮ On the minimum gap between sums of square roots of small integers ⋮ The Diophantine Equation 𝑥⁴+2𝑦⁴=𝑧⁴+4𝑤⁴ ⋮ Rational points on diagonal quartic surfaces

Uses Software

• heapsort

Cites Work

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• Average-case results on heapsort
• Integer points and the rank of Thue elliptic curves
• Euler's problem on sums of three fourth powers
• Solutions of the Diophantine Equation A 4 + B 4 = C 4 + D 4
• On A 4 + B 4 + C 4 = D 4
• Integer Points on Curves of Genus 1
• The Density of Zeros of Forms for which Weak Approximation Fails
• New results in equal sums of like powers
• Tamagawa numbers of diagonal cubic surfaces, numerical evidence
• Equal sums of four seventh powers
• A Survey of Equal Sums of Like Powers
• Equal Sums of Biquadrates
• A Counterexample to Euler's Sum of Powers Conjecture

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