2010/06/07 by Andreas-Stephan Elsenhans, Elsenhans, Andreas-Stephan, Jörg Jahnel +1
Computer Science · Mathematics · Physics and Astronomy · #14J28 #Advanced Mathematical Theories and Applications #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Chaos-based Image/Signal Encryption #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Primary 11Y50. Secondary 14G05
paper · pdf · doi:10.48550/arxiv.1006.1196
openalex publication_date 2010/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The quadruple (1 484 801, 1 203 120, 1 169 407, 1 157 520) already known is essentially the only non-trivial solution of the Diophantine equation x4 + 2 y4 = z4 + 4 w4 for |x|, |y|, |z|, and |w| up to one hundred million. We describe the algorithm we used in order to establish this result, thereby explaining a number of improvements to our original approach.