I tried to mail Peter Boucher, who posted the question, but my e-mail
bounced, so, apologies to thsoe who are not interested.
Have you read:
Bremner,A.,
On Trinomials of Type x$+n$-+Ax$+m$-+1.
Math. Scand. 49(1981) pp. 145-155.
Zbl. 458.12012.
MR 83k:12002.

Ljunggren,W.,
On the Irreducibility of Certain Trinomials and Quadrinomials.
Math. Scand. 8(1960) pp. 65-70.
.

Tverberg,H.,
On the Irreducibility of the Trinomials
x$+n$-$mpm$$x$+m$-$mpm$$1.
Math. Scand. 8(1960) pp. 121-126.

Tverberg,H.,
On Cubic Factors of Certain Trinomials.
Math. Scand. 53(1983) pp. 178-184.
Zbl. 513.12003.