I intend to maintain here a site dedicated to solutions of the diophantine equations
(4,2,2) a^{4}+b^{4}=c^{4}+d^{4}
and
(***) A^{4}-B^{4}=C^{4}-D^{4}=E^{4}-F^{4}
Before I can make the site reader friendly, you can have a look at the following files:
June 24, 2006
414.txt exhaustive list of 1009 solutions to (4,1,4) below 222,000
January 25, 2006
422-10m.txt exhaustive list of 1420 solutions to (4,2,2) below 10,000,000
January 8, 2006
mul175.txt 175 solutions to (***) below 10^{100} in multiplicative form, i.e.
by giving x_{1}, y_{1}, x_{2}, y_{2}, x_{3}, y_{3}
as described in
magic.pdf January 4, 2006
422.zip (251 KB) 11089 solutions below 10^{14} to (4,2,2)
add40.txt or
mul40.txt 40 solutions to (***) in additive or multiplicative form
high30.txt 30 more solutions to (***) in multiplicative form
magic.pdf some observations about solutions to (***)
solutions.pdf 40 solutions to (***) with many details
gaussian.pdf my personal notes (rather than clear presentation at the moment ;-(
about some conclusions from unique factorization of Gaussian integers
Jaroslaw Wroblewski
jwr@math.uni.wroc.pl