Timeline for Square free sum of two squares
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Mar 7, 2010 at 13:06 | vote | accept | CommunityBot | ||
| Mar 3, 2010 at 2:21 | comment | added | Gerry Myerson | The $b_n$ are sequence A073833 in the Online Encyclopedia of Integer Sequences, research.att.com/~njas/sequences/A073833 but none of the information there bears directly on the problems of squarefreeness or coprimality. | |
| Mar 2, 2010 at 23:39 | history | edited | user4324 | CC BY-SA 2.5 |
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| Mar 2, 2010 at 10:55 | comment | added | user4324 | Unfortunately, no! The problem at hand is the recurrence $u_0=1,\ u_{n+1}=u_n+1/u_n$ which corresponds to the two sequences $a_0=b_0=1,\ a_{n+1}=a_nb_n,\ b_{n+1}=a_n^2+b_n^2$. My conjecture is that the $b_n$'s are square free and coprime, which I am unable to (dis)prove until now! | |
| Mar 2, 2010 at 8:43 | comment | added | maks | But I think it's easy to count the number of such pairs (a,b), asymptotically. That could give an idea of "how likely" it is for a^2 + b^2 to be squarefree. I don't know if this is of any interest for you. | |
| Mar 2, 2010 at 1:09 | vote | accept | CommunityBot | ||
| Mar 2, 2010 at 20:34 | |||||
| Mar 1, 2010 at 20:48 | answer | added | Franz Lemmermeyer | timeline score: 6 | |
| Mar 1, 2010 at 20:39 | history | asked | user4324 | CC BY-SA 2.5 |