February 8th, 2014, 12:05 AM |
#41 | |

Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory | Re: Pre-Q&A Quote:
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February 8th, 2014, 12:06 AM |
#42 | |

Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 | Re: Pre-Q&A Quote:
No worries though...it's still ineresting as a factorisation. | |

February 8th, 2014, 12:10 AM |
#43 | |

Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory | Re: Pre-Q&A Quote:
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February 8th, 2014, 12:17 AM |
#44 | |

Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 | Re: Pre-Q&A Quote:
But ... If what you say is true we may be sniffing at a structure similar to the J commutative monoid. Heh he , imagine that ... | |

February 8th, 2014, 12:26 AM |
#45 | |

Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory | Re: Pre-Q&A Quote:
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February 8th, 2014, 12:39 AM |
#46 |

Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 | Re: Pre-Q&A
If you can do that thn you will probably solve the OP entirely. I'll try it too since it looks promising. |

February 8th, 2014, 12:43 AM |
#47 |

Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory | Re: Pre-Q&A
I have tried it but no dice. A negative term pops up. It's interesting that gigantic constructions are possible : (x^3 - 3x + 3)(x^8 + 4x^7 + 10x^6 + 19x^5 + 27x^4 + 25x^3 - 5x^2 - 89x - 251) = x^10 + x^9 + x^8 + x^7 + x^5 + x^4 + x^3 + x^2 + 486x - 753 Whereas we have trouble with the small ones. |

February 8th, 2014, 04:53 AM |
#48 |

Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 | Re: Pre-Q&A
Have managed a slight improvement. f(2) = 383 So we are in {0 ... 15} |

February 8th, 2014, 04:58 AM |
#49 |

Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory | Re: Pre-Q&A
Superb. {0, ..., 15} we are in now then |

February 8th, 2014, 05:10 AM |
#50 |

Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 | Re: Pre-Q&A
It looks like something magical happens when we hit consecutive coefficients of 9. You know , I found smaller coefficients using your 'generator polynomial' , (x^2 - 3x + 3) and working on the sextic , got it down to {0 ... 12} but unfortunately f(2) was not prime. Next up would be to try a 7th degree ... agentredlum predicts most coefficients of the 7th degree poly , 1 3 6 9 9 a b c |