🚀 go-pugleaf

1) Brillhart and Zierler are merely informing you that they had not, at the 
time of publication of their article, tested those T_n,k(x) for primitivity, 
only for irreducibility.  

2) The correct statement is that if f(x) is a primitive irreducible polynomial
over of degree n, then so is x^n*f(1/x) [after multiplying through to clear 
fractions].  This implies your first statement (for trinomials).  Tetranomials
can never be irreducible, much less primitive:  they are divisible by x + 1.  
This also implies that x^p + x^q + x^r + x^s + 1 primitive iff 
x^p + x^(p-s) + x^(p-r) + x^(p-q) + 1 primitive.

Robert L. Ward