[math-fun] polynomials with lots of integer roots computed in few arithmetic operations (Phil Carmody?)

In the book by Crandall & Pomerance, Phil Carmody is mentioned as having found a lot of polynomials of the form Poly(x) = (((x^2-a)^2-b)^2-c)^2-d with all 16 roots being integers. [Is it possible to get 32 integer roots at the next stage?] Might Phil inform us more about how he did that and what are these polynomials? -- Warren D. Smith http://RangeVoting.org  <-- add your endorsement (by clicking "endorse" as 1st step)