Integer Solutions to Box Optimization Problems

Building the Biggest Box: Three-factor Polynomials and a Diophantine Equation

“…However, we suspect the problem was considered even earlier in some form. The problem of finding dimensions for the rectangle that yields rational solutions has also been considered by several different authors: see Dundas [9], Coll et al [4] (who give the same solution as Dickson [6]); Graham and Roberts [11], Duemmel [8] (who confronted the same problem writing an exam as did the second author); Buddenhagen et al [2]. (Hereafter, we adopt the notation of our sources for ease of reference).…”