### Questions (190)

 8 |f| is periodic implies f is periodic 6 Every $f : [a, b] → [a, b]$ has a fixed point where $f$ is continuous. Deduce the intermediate value theorem. 5 Find complex roots of $\frac{2i}{1+i}$ 5 If $n$ is a product of primes, what is the number of divisors? 5 Solve the differential equation $\frac{dy}{dx}=\frac{2x+y}{y}$

### Reputation (2,165)

 +10 Contraction mapping with no fixed point using a incomplete metric space +10 Is every complete metric space closed? +20 Show that $\cot \frac{\pi}{2m}\cot \frac{2\pi}{2m}\cot \frac{3\pi}{2m}…\cot \frac{(m-1)\pi}{2m}=1$ +10 Prove that the union of two normal subgroups is also a normal subgroup

 1 Suppose $n|a^2-1$ Show that $n=$gcd$(a-1,n)$gcd$(a+1,n)$ 0 Poisson Process with continuous rate, Finding Conditional Number of Arrivals 0 Graph Theory, planar graph $(p,q)$ is in the form $q=\frac{n(p − 2)}{(n − 2)}$where $q$- #edges, $p$- #points

### Tags (149)

 1 modular-arithmetic × 14 0 probability × 26 1 gcd-and-lcm × 2 0 linear-algebra × 21 1 elementary-number-theory × 2 0 statistics × 21 1 prime-factorization × 2 0 real-analysis × 16 0 complex-analysis × 29 0 number-theory × 15