Bibliographic Details
| Title: |
On 2025 and Other Torn Numbers. |
| Authors: |
Javaheri, Mohammad (AUTHOR) mjavaheri@siena.edu |
| Source: |
American Mathematical Monthly. May2026, Vol. 133 Issue 5, p478-484. 7p. |
| Subject Terms: |
Prime factors (Mathematics), Number theory |
| Abstract: |
2025 is an example of a torn number, a perfect square that is a fixed point of the following split-add-square procedure: the number is torn in half (as 20 and 25), then the two parts are added together ( 20 + 25 = 45 ), and finally the result is squared ( 45 2 = 2025 ). We show that there exist at least 2 μ (k) − 1 2k-digit torn numbers, k ≥ 1 , where μ (k) is the number of prime factors of 10 k − 1 . Moreover, we show that the split-add-square procedure has infinitely many periodic points of any arbitrary period. [ABSTRACT FROM AUTHOR] |
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| Database: |
Education Research Complete |
