# user17762

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 17m comment solving ODE: $\ln(y') + (x)y' -y = 0$ @IgorRivin "often = always" 42m answered $\int_0^\pi \exp(\cos(t))\cos(\sin(t))\,dt =\pi$ 1h comment Find all rational solutions to $x^3 - y^2 = 2$. The equation $y^2 = x^3+k$, where $k \in \mathbb{Z}$ is called Mordell-Bachet equation. An excellent resource for this is Keith Conrad's article, where he discusses integer solutions. Your problem is on page $6$, theorem $3.4$. 16h comment if such$\sqrt{37}+\sqrt{47}<\dfrac{n}{m}<\sqrt{41}+\sqrt{43}$ Find this $m$ minimum I am probably missing something. How does this ensure that $n$ is an integer? 16h comment if such$\sqrt{37}+\sqrt{47}<\dfrac{n}{m}<\sqrt{41}+\sqrt{43}$ Find this $m$ minimum @chinamath Yes. Finding the minimum requires some more thought. 16h answered if such$\sqrt{37}+\sqrt{47}<\dfrac{n}{m}<\sqrt{41}+\sqrt{43}$ Find this $m$ minimum 16h reviewed Delete True/False: Differentiablity #2 16h reviewed Close Prove or disprove if L is a subgroup 16h reviewed Close Characteristic function say something about the expectation and variance 16h reviewed Close Sum of two independent random variables converges in distribution 16h reviewed Leave Open Solution book of John Kelley's , J.Munkres's 16h reviewed Close Probability of rolling 1-6 with six dice given two SELECTIVE re-rolls (From King of Tokyo) 17h answered Method of proving trignometric identities 17h answered Value of $\frac{1}{\sqrt{3}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{11}}+\frac{1}{\sqrt{11}+\sqrt{15}}+\cdots$ ($n$ terms) 17h revised Limit $\lim_{n \to \infty} n (1 - \mathrm{e}^{t/n})$ added 10 characters in body 17h comment Counting/ probability @Itzel It can be written as a permutation. Note that it can be written as $\dfrac{12!}{5!} \cdot \dfrac{15!}{8!} = P(12,7) \cdot P(15,7)$, where $P(n,r)$ is the number of ways of permuting $r$ out of $n$ objects. 17h reviewed Leave Open Evaluate the indefinite integral! 17h reviewed Leave Open $\underset{n \to \infty}{\lim} f(a_n)=0$ and also $\underset{x \to 0}{\lim} f(x)=1$ 17h reviewed Leave Open Finding limit of function $\lim_{x\to 0}(\sin^2(\frac{\pi}{2-ax}))^{\sec^2\frac{\pi}{2-bx}}$ 17h reviewed Leave Open What is the degree of following differential equations