mich95

 59 Are there any irrational numbers that have a difference of a rational number? 10 what is the greatest integer that divides $p^4-1$ for every prime number p greater than 5 10 Let $f$ be a function such that $f'(x)=\frac{1}{x}$ and $f(1) = 0$ , show that $f(xy) = f(x) + f(y)$ 9 Inequality involving Square Root 8 Is it true that $G$ is abelian?

### Reputation (7,052)

 +20 Show that any cyclic group of even order has exactly one element of order $2$ +10 $H$ Hilbert space, $S\subset H$ implies $S^\perp$ closed +10 How can I prove that there exists only one subgroup of A4 of order 4 +10 Proving gcd($a,b$)lcm($a,b$) = $|ab|$

### Questions (27)

 4 Compute $\displaystyle\lim_{n \to \infty} \sqrt{n} \int_{-1}^{1} e^{\frac{-nx^{2}}{2}}f(x) \ \mathrm dx$ [closed] 3 $\mathbb{R}$ as a $\mathbb{Z}$ module 2 cdf of a “mixed” random variable 2 Find a strictly decreasing $f:(0,1) \to [0, \infty]$ such that $f(0^{+})= \infty$, $f(1)=0$ and $f(u^2)=2 f(u)$. 2 If $\mathbb{A}$ and $\mathbb{B}$ are unital banach algebras, and $f: \mathbb{A} \to \mathbb{B}$

### Tags (177)

 161 abstract-algebra × 68 59 transcendental-numbers 109 group-theory × 40 56 calculus × 36 80 number-theory × 9 40 linear-algebra × 27 67 irrational-numbers × 5 37 real-analysis × 23 59 rationality-testing 35 functions × 15

### Accounts (2)

 Mathematics 7,052 rep 11226 Cross Validated 106 rep 4