Hello all,

Does anybody have the hardware and programming skills to find a non-trivial solution in the integers to the multi-grade eqn,

x1^k + x2^k + x3^k + x4^k + x5^k = y1^k + y2^k + y3^k + y4^k + y5^k,

for k = 1,3,5,7, where x1 = 0.

There are only two known solns, found by Letac back in 1942. A guy in sci.math.symbolic did a search and established those two are the only primitive solns (no common factor) with terms < 450. However, he could not extend the range beyond that in a reasonable amount of time.

A soln to the above eqn would imply what is called an "ideal solution" to the Prouhet-Tarry-Escott problem for deg 8 -- and would be the first new one in almost 70 years. Care to give it a shot?

- Titus

No offense, but should I conquer that problem I wont be pasting the solution here. Dont hold your breath for any PM either.

Say you submit the results and algorithm to a paper (Mathematics of Computation would be nice), but wait months for it to be published. Then someone posts a solution in a newsgroup -- ouch, there goes your priority. (With the advent of the Internet, publishing some kinds of mathematical results, like finding a new Mersenne prime, can be done in seconds.)

P.S. What's a PM?

- Titus

Private message.
No, your point isn't quite valid. Dates & databases can be altered. The question is whether a credible & verifiable trail can be substantiated by others. If one were going to post such a profound solution to the Internet, it would behoove them to do so in a credible & highly regarded venue. Doing so at a help site such as this isn't the most strategically smart decision to make (No offense to the regulars who post here...).

If this newsgroup is not the appropriate venue for a programming problem, very well, then if someone can find a solution, kindly send it to J. Meyrignac of Eulernet. He is maintaining a database of Equal Sums of Like Powers.

At least now there are more programmers aware of the problem. (What is interesting to know is how Letac found the two smallest solns back in 1942 without a computer.)

- Titus

What is the problem name ?

Problem: "Finding a new Ideal Solution to the Prouhet-Tarry-Escott Problem of Degree 8"

(There are only two known. It takes only a small transformation to make a system valid for k = 1,3,5,7 to be valid for k = 1,2,3,...8 by increasing the number of terms. Click on my name to see link to Homepage. It is in section 019.)

- Titus