as to: <CITE http://www.mathpuzzle.com/Gaussians.html> (3+13i)^3 + (7+i)^3 = (3+10i)^3 + (1+10i)^3 and (6+3i)^4 + (2+6i)^4 = (4+2i)^4 + (2+i)^4 Is there something similar for Gaussian fifth powers? See http://euler.free.fr/details.htm for details on this problem in the integers. I offer $20 for a nontrivial solution with proper Gaussian integers </CITE http://www.mathpuzzle.com/Gaussians.html> I have a parametric solution for the fifth power (at home). I'll dig it up and send the solution to the list. all the best, jj * ed pegg <ed@mathpuzzle.com> [Jan 06. 2003 20:26]:
There are various number theoretic problems in the Gaussian Integers that I haven't been able to solve.
http://www.mathpuzzle.com/Gaussians.html
If any of these matters are resolved, or if you have solutions to any of them, please let me know.
--Ed Pegg Jr, www.mathpuzzle.com
-- p=2^q-1 prime <== q>2, cosh(2^(q-2)*log(2+sqrt(3)))%p=0 Life is hard and then you die.