The identity $$\medmuskip 0mu minus 2mu \bigl((x^2-85)^2@-@@4176\bigr)^2-2880^2=(x^2-@ 1^2)\*(x^2-@ 7^2)\*(x^2-@ 11^2)\*(x^2-@ 13^2),$$ discovered by R. E. Crandall, allows the evaluation of a product of 8 integers by a succession of 3 squares and 3 subtractions. The question arises whether there exist formulas like Crandall's with more than 3 nested squares. It will be shown that this is not the case; however, there are infinitely many formulas of length 3.
"Nested squares and evaluations of integer products." Experiment. Math. 9 (3) 369 - 372, 2000.