ORCiD
0000-0003-3513-508X
Abstract
Euler’s key idea for equating the Quartic in the title to a square is to set k=P+surd(Q). From this he derives P=f·x^2 and Q=4f·y^2+4 and solves the Pell equation for y. He then discusses various extensions to rational numbers that leave k an integer. Euler provides incomplete tables for integers k with |k|square.
Last Page
62
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Recommended Citation
Ehlers, Georg
()
"On the Cases in Which the Formula x^4+kxxyy+y^4 Can Be Reduced to a Square,"
Euleriana: 4(1), pp.43-62.
DOI: https://doi.org/10.56031/2693-9908.1069
Available at:
https://scholarlycommons.pacific.edu/euleriana/vol4/iss1/3