Chegg Textbook Solutions for Mathematics for Elementary Teachers 7th Edition: Chapter 5.1

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    Six. In the 1930's Professor E. Ducci of Italy discovered that this process will always produce four zeros.* Some sets of four numbers require more steps than others. For example, 1, 2, 5 and 10 requires nine squares before obtaining all zeros. This suggests other questions to investigate: Is there a set of four integers such that 10 squares are required to obtain all zeros? Is there a set of four integers such that k squares are required to obtain all zeros for every whole number k? Is there a largest whole number k such that any set of four integers will require less than k squares before producing all zeros?

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