Lesson plan
Transposable integer
In mathematics, the transposable integers are integers that permute or shift cyclically when they are multiplied by another integer 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 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.
Article summary
In mathematics, the transposable integers are integers that permute or shift cyclically when they are multiplied by another integer 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 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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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.