The density of primes dividing a particular non-linear recurrence sequence
The original abstract is good, except for the second phrase which could be more precise, so here is the original abstract: ``Define the sequence \(\{b_n\}\) by \(b_0=1,b_1=1,b_2=2,b_3=1\), and NEWLINE\[NEWLINEb_n=\begin{cases} \frac{b_{n-1}b_{n-3}-b_{n-2}^2}{b_{n-4}}&\text{ if }n\not\equiv 0\pmod 3, \\ \frac{b_{n-1}b_{n-3}-3b_{n-2}^2}{b_{n-4}}&\text{ if }n\equiv 0\pmod 3\end{cases}.NEWLINE\]NEWLINE We relate this sequence \(\{b_n\}\) to the coordinates of points on the elliptic curve \(E:y^2+y=x^3-3x+4\). We use Galois representations attached to \(E\) to prove that the density of primes dividing a term in this sequence is equal to \(\frac{179}{336}\). Furthermore, we describe an infinite family of elliptic curves whose Galois images match that of \(E\).''NEWLINENEWLINEI would change this phrase ``We relate this sequence \(\{b_n\}\) to the coordinates of points on the elliptic curve \(E:y^2+y=x^3-3x+4\).'' by: We relate this sequence \(\{b_n\}\) to the coordinates of points in the group generated by P(4,7) on the elliptic curve \(E:y^2+y=x^3-3x+4\).
scientific article; zbMATH DE number 6654749