Re: [math-fun] factoring almost completely monic polynomials
What are the cases you know that don't work? --Dan Erich wrote: << for integers m and n, i've been factoring (over the integers) the polynomials: P = (x^n-1) / (x-1) - m obviously when m = (k^n-1)/(k-1) for some integer k, there is a linear factor. i'm interested in the cases when P factors without a linear factor. i've only found 6 cases: [details re 5, 6, 8, 9, 11, 14 omitted] is there some rhyme or reason for these, or are they just random?
_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele
What are the cases you know that don't work?
for integers m and n, i've been factoring (over the integers) the polynomials:
P = (x^n-1) / (x-1) - m
obviously when m = (k^n-1)/(k-1) for some integer k, there is a linear factor.
i'm interested in the cases when P factors without a linear factor. i've only found 6 cases:
is there some rhyme or reason for these, or are they just random?
i've checked |m| < 135 and n < 250, and found only those 6 examples. erich
It might be useful to see any cases where there was a linear factor, but the cofactor split further. Rich --------------- Quoting Erich Friedman <efriedma@stetson.edu>:
What are the cases you know that don't work?
for integers m and n, i've been factoring (over the integers) the polynomials:
P = (x^n-1) / (x-1) - m
obviously when m = (k^n-1)/(k-1) for some integer k, there is a linear factor.
i'm interested in the cases when P factors without a linear factor. i've only found 6 cases:
is there some rhyme or reason for these, or are they just random?
i've checked |m| < 135 and n < 250, and found only those 6 examples.
erich
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