Nested squares and evaluations of integer products
Dilcher, Karl
Experiment. Math., Tome 9 (2000) no. 3, p. 369-372 / Harvested from Project Euclid
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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.
Publié le : 2000-05-14
Classification:  11C08,  11Y05 
@article{1045604671,
     author = {Dilcher, Karl},
     title = {Nested squares and evaluations of integer products},
     journal = {Experiment. Math.},
     volume = {9},
     number = {3},
     year = {2000},
     pages = { 369-372},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1045604671}
}

Dilcher, Karl. Nested squares and evaluations of integer products. Experiment. Math., Tome 9 (2000) no. 3, pp.  369-372. http://gdmltest.u-ga.fr/item/1045604671/