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### Questions (15)

 17 How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition? 14 Is $\mathbb{Q}/\mathbb{Z}$ isomorphic to $\mathbb{Q}$? 10 Counterexample: $G \times K \cong H \times K \implies G \cong H$ 3 Solve $-B \ln y -A y \ln y + A y- A =0$ for $y$ 3 Integrate: $\int\limits_0^\infty{\frac{x^{n-2}}{b\left(1+ ~a x^{\frac{n-1}{n-2}}\right)} \sin{(x b)}~ dx}$

### Reputation (486)

 +20 Is $\mathbb{Q}/\mathbb{Z}$ isomorphic to $\mathbb{Q}$? +5 How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition? +5 Show $\prod \limits_{\substack{k=0\\k\neq k_0}}^{K-1}\left(\exp\left[{\frac{2 \pi i (k-k_0)}{K}}\right]-1\right)=(-1)^{K-1} K$ +5 Counterexample: $G \times K \cong H \times K \implies G \cong H$

 4 Examples of nonabelian groups.

### Tags (21)

 4 group-theory × 6 0 gamma-function × 4 4 abstract-algebra × 3 0 complex-analysis × 4 4 finite-groups × 3 0 elementary-number-theory × 3 4 big-list 0 calculus × 3 4 examples-counterexamples 0 transcendental-equations × 2

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 Mathematics 486 rep 318 Mathematica 135 rep 5 Stack Overflow 115 rep 4 Physics 111 rep 5 Super User 101 rep 4