Some general results and open questions on palintiple numbers (Q2926267)

The author studies the set of ``palintiples''. These are natural integers which are integer multiples of their digit reversals. Here are two examples in base 10: \(87912=4\cdot 21978\) and \(98901=9\cdot 10989\). Carry considerations naturally lead to a partition of the set of palintiples into three classes, called symmetric, shifted-symmetric and asymmetric palintiples. He determines the set of 5-digit symmetric palintiples (the term ``symmetric'' refers to the carry structure), and completely identifies the set of shifted-symmetric palintiples (where the carry structure is symmetric but shifted by one position). In the paper, some questions posed by \textit{L. Pudwell} [Math. Mag. 80, No. 2, 129--132 (2007; Zbl 1227.11034)] are answered. Finally, the author shows some connections of palintiples with so-called ``palinomials'' (polynomials whose coefficients are based upon the digits within palintiples) and roots of unity. The proofs are elementary.