February 6th, 2014, 05:26 AM  #11 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,179 Thanks: 180  Re: PreQ&A
You and I are thinking alike in this matter , i also tried x^5 + x + 1 and x^4 + x^2 + 1 , then attempted to find other poly's similar , came close with x^9 + 2x + 3 but alas 519 = 3*173 ... composite Then i made a list of primes 520 < p < 588 and fooled around with No success. I'm doing this with no programming usage ability so by now i am quite tired of editing WIA entries and pressing = every time. BTW , I can't find anything i can see about Schur's Theorem that is relevent to CRG's claim in the other thread. Found this but i'm not sure if it applies. http://en.m.wikipedia.org/wiki/Cohn's_i ... _criterion 
February 6th, 2014, 05:38 AM  #12  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: PreQ&A Quote:
 
February 6th, 2014, 05:49 AM  #13  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,179 Thanks: 180  Re: PreQ&A Quote:
Where f(10) = 5 , f(2) = 5 and f(5) = 1 ?  
February 6th, 2014, 05:50 AM  #14 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: PreQ&A
I doubt.

February 6th, 2014, 05:54 AM  #15  
Math Team Joined: Apr 2010 Posts: 2,770 Thanks: 356  Re: PreQ&A
This is why I thought Schur's theorem could be applied here Quote:
f(2) is prime so perhaps, all coefficients of f are in {0, 1,...,9} so the polynomial is irreducible. But perhaps since it is about x = 2 instead of x = 10 it works for coeficients in {0, 1, 2} only. You have similar observations. Maybe the answer to the bonus question would then be "to mislead "us" (me at least)"  
February 6th, 2014, 05:55 AM  #16 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,179 Thanks: 180  Re: PreQ&A
Yeah , you're right. f(10) = 5 would mean we need negative coefficients ...€¥§¿!! 
February 6th, 2014, 06:05 AM  #17  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,179 Thanks: 180  Re: PreQ&A Quote:
 
February 6th, 2014, 06:12 AM  #18  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: PreQ&A Quote:
 
February 6th, 2014, 06:17 AM  #19 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,179 Thanks: 180  Re: PreQ&A
[Deleted Joke]

February 6th, 2014, 08:24 PM  #20  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 932 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: PreQ&A Quote:
It gets worse: it looks like I mixed up my inequalities when posting this question, and I should have allowed 0..10 rather than 0..9. Those of you who suspected the problem was unsolvable were probably right... but I have it on good authority that the problem with 0..10 is solvable. Quote:
 