Talk:Polydivisible number
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Reliable sources / inline citations?
[edit]I noticed there are no citations for specific facts mentioned in this article -- for example, the claim of the exact number of all polydivisible numbers in existence, with no link to a proof that none larger exist or anything else substantial. The sources give a list of "all" polydivisible numbers (which is just a list of numbers, with no other text) and an article about the nine-digit problem. I attempted to find a better source on Google Scholar, but found no relevant results -- in fact almost no results at all for the term 'polydivisible number', indicating this is not even necessarily a standard mathematical term. I question therefore the reliability of this article and wonder if I should put flags on it indicating this -- but am going to double-check the relevant Wikipedia standards before doing so. (Whoops almost forgot my signature) Liger42 (talk) 20:08, 31 January 2014 (UTC)
(edit: I suppose it is "obvious" that every polydivisible number of length n>1 has as its start a polydivisible number of length n-1, indicating the number should decrease and eventually reach 0, but this is original research on my part, i.e. i just pulled it out of my head.) — Preceding unsigned comment added by Liger42 (talk • contribs) 20:11, 31 January 2014 (UTC)
Interesting numbers in different bases
[edit]With regards to 381654729 being the only solution in base 10 which uses every digit only once, I decided to generalise it to see what solutions exists in other bases.
E.g. in base 6 the only one polydivisible number which uses the numbers 1-5 is 14325_6..
Below are some more solutions
| Base | Solutions (complete up to base 10) |
|---|---|
| 2 | 12 |
| 3 | No solution (an error in my program allowed odd bases to have solutions) |
| 4 | 1234
3214 |
| 5 | No solution (an error in my program allowed odd bases to have solutions) |
| 6 | 143256
543216 |
| 7 | No solution (an error in my program allowed odd bases to have solutions) |
| 8 | 32541678
52347618 56743218 |
| 9 | No solution (an error in my program allowed odd bases to have solutions) |
| 10 | 38165472910 |
| 11 | No solution (an error in my program allowed odd bases to have solutions) |
| 12 | No solution. |
| 13 | No solution (an error in my program allowed odd bases to have solutions) |
| 14 | 9C3A5476B812D14 |
| 15+ | No solution |
DC (talk) 10:39, 24 October 2016 (UTC)
See (sequence A163574 in the OEIS), there may be no solution for any base b > 14.
Besides, your list is not right: 123 is 510, which is not divisible by 2.