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Previous work showed that there are nine essentially distinct $(a,b,c,r,s)$ for which $N \\ge 4$, except possibly for cases in which the solutions have $r$, $a$, $x$, $s$, $b$, and $y$ each bounded by $8 \\cdot 10^{14}$ or $2 \\cdot 10^{15}$. In this paper we show that there are no further cases with $N \\ge 4$ within these bounds. 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