
Re: a^5+b^5+c^5+d^5+e^5 = f^5
Posted:
Aug 15, 2006 5:29 PM


http://euler.free.fr/
Tapio
"James Waldby" <jwaldby@pat7.com> wrote in message news:44E1ED1B.BD347C2D@pat7.com... > titus_piezas@yahoo.com wrote: > ... >> A small summary, you found the first solution to a 5th power >> decomposable as five positive 5th powers in two ways, namely, > [744^5] > >> Second, it is known there are solutions to >> 2a^4+2b^4+c^4 = d^4 >> >> Turns out there are for 5th powers as well, >> 2a^5+2b^5+c^5 = d^5 >> >> (526, 526, 1349, 1349, 1355; 1685) >> >> P.S. Remember, there are no solutions yet for 8.4.4. ;) > > I hadn't noticed that entry (526, 526, 1349, 1349, 1355; 1685) > and haven't seen any other solutions like it yet. My program > http://pat7.com/jp/515count6d.c with f<10007 has been running > for about 22 hours and has found 338 solutions so far, listed > in http://pat7.com/jp/s51510007338 and in variant forms in > files t, u, v 51510007338 at same site. For example, > http://pat7.com/jp/v51510007338 lists selections where f (in > a^n + b^n + c^n + d^n + e^n = f^n) appears in multiple lines. > For example, the entries > 1921< 1921 2042 2398 2920 3839 4120 > 1921> 275 351 872 1298 1855 1921 > 1921> 95 771 1020 1519 1756 1921 > show that 4120^5 can be written two ways as the sum > of 9 fifth powers. Far more common are entries like > 4228< 432 519 875 4228 6921 7035 > 4228> 584 593 2383 2392 4126 4228 > from which 7035^5 can be written as the sum of 5 or 9 > fifth powers. > jiw

