Short & Sweet Math Challenge #21: Powers that be

[Valentin Albillo]

 
Hi, J-F:

(11-06-2016 05:21 PM)J-F Garnier Wrote:  Well, I tried first on Emu71, then switched to Free42 to have higher computing accuracy, but I'm afraid I wasn't able to build a proper solution with either tool.

With Emu71, I was able to find the roots, but wasn't able to identify all the constants with the desired property due to the limited accuracy.

How many did you identify ? How do you know they aren't all ?

For the particular limits of this challenge, i.e.: minimal polynomials up to degree 8 (or less) and with coefficients -1,0,+1, I found no accuracy problems at all (though perhaps there are and I just didn't find them ... 8-D  )

Quote:And with Free42, I had the right accuracy, but had difficulties to find the roots of the polynomials.

How so ? Details ?

Quote:Waiting for your solution...

I'll post it within two days, give or take a day. It does take a significant amount of time to write down the solution post and regrettably it seems there wasn't much interest at all, no one but you and Gerson made any attempt at a solution or posted comments, let alone post actual code.

Thanks for your interest.

Best regards.
V.