Timeline for Can the product of two disjoint subsets of numbers like 7, 77, 777, ... be equal?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 10 at 10:48 | comment | added | dEmigOd | @pts, now I understand the answer. | |
| Jan 10 at 9:45 | comment | added | pts | An even simpler proof: Let's suppose it's possible. The two products are equal, so they are equal modulo 4 as well. 7 is 3 modulo 4, all other numbers are 1 modulo 4 (because they end in 77). Thus one of the products containing 7 is $3\cdot1\cdot1\cdot\ldots=3$ modulo 4, and the other product is $1\cdot1\cdot1\cdot\ldots=1$ modulo 4. This is a contradiction, so it's impossible to have such products. | |
| Jan 8 at 21:18 | vote | accept | Iulian Serbanoiu | ||
| Jan 8 at 4:43 | history | edited | Timothy Chow | CC BY-SA 4.0 |
improved formatting
|
| Jan 7 at 21:50 | history | answered | Aleksei Kulikov | CC BY-SA 4.0 |