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# 52 Accepts

 Apr 16 accepted Show that $\mathrm{SO}_3(\mathbb{Q}_p) \simeq \mathrm{SL}_2(\mathbb{Q}_p)$ Apr 15 accepted How do I get $\int_0^1 \frac{dz}{\sqrt{z(z - 1\,)(z+1\,)}} = \frac{\sqrt{\pi}}{2} \frac{\Gamma(\frac{3}{4})}{\Gamma(\frac{9}{4})}$? Mar 22 accepted equivalent to $A \to (C \leftrightarrow D)$ Feb 4 accepted How to derive $\sum_{n=0}^\infty 1 = -\frac{1}{2}$ without zeta regularization Jan 29 accepted Does $\overline{ \sqrt{1 + i}} = \sqrt{1-i} \$? Jan 26 accepted express as contour integral $f(x) = \int_0^\infty dt \; e^{-t/g} \; \frac{1}{\sqrt{1 - 2 t x}}$ Jan 10 accepted What is the minimum polynomial of $x = \sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{6} = \cot (7.5^\circ)$? Jan 6 accepted Prove there are infinitely many primes in $\mathbb{Z}[i]$ Dec 26 accepted How do I simplify: $\exp \left(-a \frac{\log x}{\log Q} \right)$? Dec 23 accepted What is $\frac{1}{1+\sqrt[3]{2}}$ in $\mathbb{Q}(\sqrt[3]{2})$? Dec 22 accepted Show $a^2 + b^2 + 1 \equiv 0 \mod p$ always has a solution if $p = 4k+3$ Dec 22 accepted Does $f''(0^+)=f''(0^-)$? Dec 16 accepted Is there a special value for $\frac{\zeta'(2)}{\zeta(2)}$? Dec 7 accepted $10^9 \times \sqrt{3}$ what are first two digits after the decimal point? Nov 27 accepted Alternative definition of Gamma function. Show that $\lim_{n \to \infty} \frac{n! \; n^m}{m \times (m+1) \times \dots \times (m+n)} = (m-1)!$ Nov 22 accepted Do the adeles $\mathbb{A}$ have the same cardinality as the real numbers $\mathbb{R}$? Nov 16 accepted How to estimate $\left(1 + \sqrt{2} + \sqrt{3} + \dots + \sqrt{n} \right) - \frac{2}{3} n \sqrt{n}$? Aug 26 accepted Large regions of the plane $(x,y) \in \mathbb{Z}^2$ with no relatively prime points: $\mathrm{gcd}(x,y) > 1$ Aug 19 accepted Prove or disprove: $\sum_{b \vee d = x} \tau(b) \tau(d) = \tau(x)^3$ Jul 30 accepted Computing the intersection of two arithmetic sequences $(a\mathbb{Z} + b) \cap (c \mathbb{Z} + d)$