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A permutiple is a number which is an integer multiple of some permutation ofits digits. A well-known example is 9801 since it is an integer multiple of itsreversal, 1089. In this paper, we consider the permutiple problem in anentirely different setting: continued fractions. We pose the question of whenthe simple continued fraction representation of a rational number is an integermultiple of a permutation of its partial quotients (or digits, as we shall callthem). We develop some general results and apply them to finding new examples.In doing so, we attempt to classify all 2, 3, and 4-digit continued fractionpermutiples in terms of basic permutiple types which we discover along the way.We also generate new examples from old by finding conditions which guaranteethat digit-string concatenation yields other permutiples.

Digit Preserving Multiplication in Continued Fraction Representations