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 Nov23 awarded Yearling Sep30 awarded Explainer Sep24 awarded Autobiographer Jun27 comment Show $\lim_{n_\rightarrow \infty}\int_0^\infty ne^{-\frac{2n^2x^2}{x + 1}}dx = \infty$ (Oops, my comment had a silly mistake.) Your answer quite decisively settles the issue. Nov23 awarded Yearling May1 awarded Nice Answer Mar28 comment Limit of the ratio of the logs, knowing the ratio I'd be surprised if you could say much about the relationship between the two ratios in general. Mar28 comment Limit of the ratio of the logs, knowing the ratio Not necessarily: consider $f(x)=x^a$, $g(x)=x^b$ with $ab$ the first limit is $\infty$ but the second limit will be $a/b$ - this we can achieve any positive value for the second limit. If $f(x)=e^x$ and $g(x)=x$ then both limits are $\infty$. Nov23 awarded Yearling Apr27 answered Reference for general-topology Dec27 awarded Nice Answer Nov23 awarded Yearling Jul1 awarded Necromancer Jul1 awarded Revival Apr18 comment On the equation $3a^2-4b^3=7^c$ BTW Twh article "Computing integral points on Mordellâ€™s elliptic curves" by Gebel, Petho, Zimmer shows that the torsion groups are trivial (Prop.3.1) and the article may give the tools to complete the proof of the result. Apr1 answered A generic question on stochastic integrals Apr1 answered On the equation $3a^2-4b^3=7^c$ Mar31 answered Logical reason for the intersection of an infinite family of open sets not being necessarily open Mar31 comment On the equation $3a^2-4b^3=7^c$ There are solutions beyond the trivial $(\pm1,-1,1)$, for example $(\pm13,5,1)$, as well as families of solutions --- if $(a,b,c)$ is a solution, then clearly $(a\cdot 7^{3m}, b\cdot 7^{2m}, c+6m)$ is also a solution for $m>0$.