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Statements

Subject Item
dbr:Transposable_integer
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Transposable integer Entier transposable
rdfs:comment
Les chiffres de certains entiers spécifiques permutent ou se décalent circulairement quand ils sont multipliés par un nombre n. Voici quelques exemples: * 142857 × 3 = 428571 (décalage circulaire d'un chiffre à gauche) * 142857 × 5 = 714285 (décalage circulaire d'un chiffre à droite) * 128205 × 4 = 512820 (décalage circulaire d'un chiffre à droite) * 076923 × 9 = 692307 (décalage circulaire de deux chiffres à gauche) The digits of some specific integers permute or shift cyclically when they are multiplied by a number n. Examples are: * 142857 × 3 = 428571 (shifts cyclically one place left) * 142857 × 5 = 714285 (shifts cyclically one place right) * 128205 × 4 = 512820 (shifts cyclically one place right) * 076923 × 9 = 692307 (shifts cyclically two places left) These specific integers, known as transposable integers, can be but are not always cyclic numbers. The characterization of such numbers can be done using repeating decimals (and thus the related fractions), or directly.
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Les chiffres de certains entiers spécifiques permutent ou se décalent circulairement quand ils sont multipliés par un nombre n. Voici quelques exemples: * 142857 × 3 = 428571 (décalage circulaire d'un chiffre à gauche) * 142857 × 5 = 714285 (décalage circulaire d'un chiffre à droite) * 128205 × 4 = 512820 (décalage circulaire d'un chiffre à droite) * 076923 × 9 = 692307 (décalage circulaire de deux chiffres à gauche) Ces entiers spécifiques, appelés entiers transposables sont parfois des nombres cycliques. On peut caractériser ces nombres en utilisant des développements décimaux périodiques (et donc les fractions liées), ou directement. The digits of some specific integers permute or shift cyclically when they are multiplied by a number n. Examples are: * 142857 × 3 = 428571 (shifts cyclically one place left) * 142857 × 5 = 714285 (shifts cyclically one place right) * 128205 × 4 = 512820 (shifts cyclically one place right) * 076923 × 9 = 692307 (shifts cyclically two places left) These specific integers, known as transposable integers, can be but are not always cyclic numbers. The characterization of such numbers can be done using repeating decimals (and thus the related fractions), or directly.
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