Abstract
We give a complete description of all solutions to the equation f13 + f 23 = f 33 + f 43 for quadratic forms fj [x,y] and show how Ramanujan's example can be extended to three equal sums of pairs of cubes. We also give a complete census in counting the number of ways a sextic p [x,y] can be written as a sum of two cubes. The extreme example is p(x,y) = xy(x4 - y4), which has six such representations.
Original language | English (US) |
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Pages (from-to) | 761-786 |
Number of pages | 26 |
Journal | International Journal of Number Theory |
Volume | 17 |
Issue number | 3 |
DOIs | |
State | Published - Apr 2021 |
Keywords
- Cubic forms
- diophantine equations
- sextic forms
ASJC Scopus subject areas
- Algebra and Number Theory