Timeline for What are the smallest positive $a,b,c$ for which $a/(b+c)+b/(a+c)+c/(a+b)$ is an integer $>2$?
Current License: CC BY-SA 4.0
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| Nov 23, 2018 at 3:04 | comment | added | Christopher D. Long | I finished my rank 4 code, and it found that N=13502 has lowest height solution with max(a,b,c) having 1322 digits, which is quite a bit larger than the above solution. The code and calculation are here: github.com/octonion/puzzles/blob/master/twitter/fruits/… | |
| Nov 22, 2018 at 22:41 | comment | added | François Brunault | I computed with Magma the 2-Selmer groups of these curves (maybe under GRH) and the smallest $N$ such that $E$ has rank 4 indeed seems to be 13502 (I restricted to those curves with root number $+1$ so the parity conjecture is also used). There is a conjecture of Lang asserting that the size of the smallest non-torsion point of an elliptic curve is bounded from below by an absolute constant times the size of the minimal discriminant (which here is polynomial in $N$). | |
| Nov 22, 2018 at 17:07 | history | asked | Christopher D. Long | CC BY-SA 4.0 |