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- W4297670631 abstract "A permutiple is a number which is an integer multiple of some permutation of its digits. A well-known example is 9801 since it is an integer multiple of its reversal, 1089. In this paper, we consider the permutiple problem in an entirely different setting: continued fractions. We pose the question of when the simple continued fraction representation of a rational number is an integer multiple of a permutation of its partial quotients (or digits, as we shall call them). 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 fraction permutiples in terms of basic permutiple types which we discover along the way. We also generate new examples from old by finding conditions which guarantee that digit-string concatenation yields other permutiples." @default.
- W4297670631 created "2022-09-30" @default.
- W4297670631 creator A5075604051 @default.
- W4297670631 date "2017-02-15" @default.
- W4297670631 modified "2023-09-30" @default.
- W4297670631 title "Digit Preserving Multiplication in Continued Fraction Representations" @default.
- W4297670631 doi "https://doi.org/10.48550/arxiv.1702.04760" @default.
- W4297670631 hasPublicationYear "2017" @default.
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