#### Vol. 3, No. 4, 2010

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Some conjectures on the maximal height of divisors of $x^n-1$

### Nathan C. Ryan, Bryan C. Ward and Ryan Ward

Vol. 3 (2010), No. 4, 451–457
##### Abstract

Define $B\left(n\right)$ to be the largest height of a polynomial in $ℤ\left[x\right]$ dividing ${x}^{n}-1$. We formulate a number of conjectures related to the value of $B\left(n\right)$ when $n$ is of a prescribed form. Additionally, we prove a lower bound for $B\left(n\right)$.

##### Keywords
cyclotomic polynomials, heights
##### Mathematical Subject Classification 2000
Primary: 11C08, 11Y70, 12Y05