Digit Reversal Without Apology

Abstract

In 1966, Alan Sutcliffe published an introductory paper on "numbers which are multiplied when their digits are reversed". Two years later T. J. Kaczynski extended Sutcliffe's work to show that there exists a 3 digit number in base n with this property if and only if there exists a 2 digit base n number with this property. This paper attempts to generalize Kaczynski's proof to the case of 4 and 5 digit integers and explores some unexpected consequences of this generalization.