### Questions (142)

 8 Suppose $\alpha, \beta>0$. Compute: $\int_{0}^{\infty}\frac{\cos (\alpha x)-\cos (\beta x)}{x}dx$ 7 Differentiability of $G(x)=\int_{\mathbb R} e^{tx}f(t)dt$ on $(0,1)$ 6 What is the intuition behind the law of quadratic reciprocity? 6 Suppose that $G$ is a group of order $924=2^2\cdot3\cdot7\cdot 11$. Prove that $G$ has an element of order $77$. 5 Real roots of $1+\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+\cdots +\frac{x^n}{n!}$ [duplicate]

### Reputation (4,594)

 +10 Suppose $\alpha, \beta>0$. Compute: $\int_{0}^{\infty}\frac{\cos (\alpha x)-\cos (\beta x)}{x}dx$ +10 Problem 7.3 I. Martin Isaacs's Character Theory Of Finite Groups +10 Normal Hall subgroups of $M$-groups are $M$-groups. +10 Exercise 6.21 Isaacs's Character theory of finite groups

 6 Evaluate the limit the following series 6 Evaluate $\sum_{k=0}^n {{2n + 1}\choose {2k + 1}}$ 6 Finding all the ideals of $\mathbb{Z} [x]/(2, (x^3+1))$? 5 What is the difference between $\Bbb F_4$ and $\Bbb Z/4\Bbb Z$ 4 Classifying all non-abelian groups of order $55$

### Tags (143)

 56 abstract-algebra × 72 11 limits × 10 21 group-theory × 29 10 combinatorics × 6 16 ring-theory × 9 10 finite-fields × 6 13 real-analysis × 42 9 sequences-and-series × 6 11 calculus × 18 9 discrete-mathematics × 2

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