Re: [math-fun] factoring almost completely monic polynomials

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