On polynomial pairs of integers
Ezerman, Martianus Frederic
Date of Issue2015
School of Physical and Mathematical Sciences
The reversal of a positive integer A is the number obtained by reading A backwards in its decimal representation. A pair (A, B) of positive integers is said to be palindromic if the reversal of the product A × B is equal to the product of the reversals of A and B. A pair (A, B) of positive integers is said to be polynomial if the product A × B can be performed without carry. In this paper, we use polynomial pairs in constructing and in studying the properties of palindromic pairs. It is shown that polynomial pairs are always palindromic. It is further conjectured that, provided that neither A nor B is itself a palindrome, all palindromic pairs are polynomial. A connection is made with classical topics in recreational mathematics such as reversal multiplication, palindromic squares, and repunits.
Journal of integer sequences
© 2015 The Author(s). This paper was published in Journal of Integer Sequences and is made available as an electronic reprint (preprint) with permission of The Author(s). The published version is available at: [https://cs.uwaterloo.ca/journals/JIS/VOL18/Ezerman/eze3.html]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.