ZFR

### Questions (538)

 17 Sum of series $\sum \limits_{k=1}^{\infty}\frac{\sin^3 3^k}{3^k}$ 14 Number which is simultaneously sum of 2 and 3 squares [closed] 12 Solve an equation of 4th degree 11 Infinite group has infinitely many subgroups, namely cyclic subgroups. 8 Problem 30 from Shakarchi Stein's book

### Reputation (5,369)

 +5 Euler-Vein diagramm +5 Irreducibility of polynomials over some quadratic fields -2 “Some examples of the Galois correspondence” lecture notes of K.Conrad +5 Integral through complex methods $\int_{0}^{2\pi}\log \sin^{2}2\theta d\theta=4\int_{0}^{\pi}\log \sin\theta d\theta=-4\pi \log 2$

 14 $A+B+C+7$ is perfect square where $A,B,C$ numbers with repeating digits. 10 Looking for a non-combinatorial proof that $a! \cdot b! \mid (a+b)!$ 10 If $\lim_{x \to \infty} (f(x)-g(x)) = 0$ then $\lim_{x \to \infty} (f^2(x)-g^2(x)) = 0\$: False? 6 If $\varphi(mn)=\lambda \varphi(m)\varphi(n)$ what should be written for $\lambda$ 5 How to prove or disprove $\forall x\in\Bbb{R}, \forall n\in\Bbb{N},n\gt 0\implies \lfloor\frac{\lfloor x\rfloor}{n}\rfloor=\lfloor\frac{x}{n}\rfloor$.

### Tags (130)

 23 elementary-number-theory × 7 11 divisibility × 3 20 real-analysis × 237 11 factorial × 2 20 number-theory × 21 10 sequences-and-series × 20 14 calculus × 6 10 binomial-coefficients × 3 11 proof-verification × 79 10 alternative-proof

### Accounts (2)

 Mathematics 5,369 rep 31540 MathOverflow 128 rep 4