We call a polynomial monogenic if a root θ has the property that Z[θ] is the full ring of integers in Q(θ). Using the Montes algorithm, we find sufficient conditions for x n + ax + b and x n + cx n−1 + d to be monogenic (this was first studied by Jakhar, Khanduja, and Sangwan using other methods). Weaker conditions are given for n = 5 and n = 6. We also show that each of the families x n + bx + b and x n + cx n−1 + cd are monogenic infinitely often and give some positive densities in terms of the coefficients.
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