Timeline for Sequences satisfying gcd(S(x), S(y)) = S(gcd(x,y))
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 28, 2013 at 15:06 | vote | accept | yrudoy | ||
| May 25, 2013 at 18:54 | answer | added | Joe Silverman | timeline score: 8 | |
| May 25, 2013 at 18:35 | comment | added | Alvin | well, those sequences satisfy the first property but not the second one. For example, if $p|a^{p-2}-b^{p-2}$ then $p|a-b,$ which holds only for finitely many $p.$ | |
| May 25, 2013 at 18:28 | comment | added | Gerhard Paseman | There are many such sequences, a^n - 1 being a form which leads to the study of cyclotomic polynomials. The Fibonacci numbers (and certain other solutions of recurrences) are a disguised form of a^n - b^n, and also have the property. I do not know the most general form of such sequences. Gerhard "Ask Me About System Design" Paseman, 2013.05.25 | |
| May 25, 2013 at 17:11 | history | asked | yrudoy | CC BY-SA 3.0 |