Journal of Integer Sequences, Vol. 18 (2015), Article 15.3.5 |

Division of Mathematical Sciences

School of Physical and Mathematical Sciences

Nanyang Technological University

21 Nanyang Link

Singapore 637371

Bertrand Meyer and Patrick Solé

Telecom ParisTech

46 rue Barrault

75634 Paris Cedex 13

France

**Abstract:**

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.

(Concerned with sequences A002778 A002779 A004023 A062936 A156317.)

Received
October 29 2012; revised version received August 5 2014; February 14 2015.
Published in *Journal of Integer Sequences*, February 14 2015.

Return to