Timeline for Numbers $n$ whose representation as the product of two divisors require more digits than that of $n$
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 26, 2022 at 9:14 | comment | added | Nilotpal Kanti Sinha | @ManfredWeis The answer to your question is yes. The smallest example is $4 \times 22 = 88$ and all these three are wasteful numbers | |
| Feb 28, 2022 at 4:51 | vote | accept | Nilotpal Kanti Sinha | ||
| Feb 28, 2022 at 4:51 | |||||
| Feb 28, 2022 at 1:21 | answer | added | user7868 | timeline score: 4 | |
| Feb 28, 2022 at 1:10 | comment | added | user7868 | Every wasteful number $n$ must be its own lexicographically greatest divisor: otherwise, given any divisor $a$, if $n=n_1n_2$ where $n_1$ is $f(a)$ digits and $n_2$ is $f(n)-f(a)$ digits, we have $n \ge 10^{f(n)-f(a)} n_1 \ge 10^{f(n)-f(a)} a$. Thus if $n=ab$, we have $f(b) \ge f(10^{f(n)-f(a)})=f(n)-f(a)+1$. | |
| Feb 27, 2022 at 17:12 | history | edited | Nilotpal Kanti Sinha | CC BY-SA 4.0 |
deleted 2 characters in body
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| Feb 27, 2022 at 14:38 | comment | added | Manfred Weis | Suggestion for an additional question: can the product of two wasteful numbers that are not primes be wasteful? | |
| Feb 27, 2022 at 14:36 | comment | added | Manfred Weis | why isn't $1$ wasteful, $1=1\cdot 1$? I would suggest not to consider $1$ as a factor. | |
| Feb 27, 2022 at 10:51 | review | Close votes | |||
| Mar 4, 2022 at 3:09 | |||||
| Feb 27, 2022 at 6:37 | history | edited | Nilotpal Kanti Sinha | CC BY-SA 4.0 |
edited body
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| Feb 27, 2022 at 6:30 | history | asked | Nilotpal Kanti Sinha | CC BY-SA 4.0 |