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2000 Nested squares and evaluations of integer products
Karl Dilcher
Experiment. Math. 9(3): 369-372 (2000).

Abstract

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.

Citation

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Karl Dilcher. "Nested squares and evaluations of integer products." Experiment. Math. 9 (3) 369 - 372, 2000.

Information

Published: 2000
First available in Project Euclid: 18 February 2003

zbMATH: 0967.11003
MathSciNet: MR1795308

Subjects:
Primary: 11C08
Secondary: 11Y05

Rights: Copyright © 2000 A K Peters, Ltd.

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Vol.9 • No. 3 • 2000
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