Geodesic
On Some Special Factorizations of (1-xn)/(1-x)
Canadian mathematical bulletin, Tome 9 (1966) no. 4, pp. 421-426

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Let A: a1 < a2 < ... < ak be a set of non-negative integers We call the corresponding polynomial the characteristic polynomial, or briefly, the c-polynomial of A. Any polynomial of such a form we call a c-polynomial and any factorization of a c-polynomial into others of the kind we call a c-factorization. If a c-polynomial cannot be factored in this way we call it c-irreducible. In this note we will determine all c-factorizations of the polynomial 1 + x + x2 + ... + xn-1, and will find under what circumstances the c-irreducible factors are also irreducible in the usual sense, i.e., irreducible over the field of rationals. 
Carlitz, L.; Moser, L. On Some Special Factorizations of (1-xn)/(1-x). Canadian mathematical bulletin, Tome 9 (1966) no. 4, pp. 421-426. doi: 10.4153/CMB-1966-050-1
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     title = {On {Some} {Special} {Factorizations} of (1-xn)/(1-x)},
     journal = {Canadian mathematical bulletin},
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     year = {1966},
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     number = {4},
     doi = {10.4153/CMB-1966-050-1},
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