Mathematics
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8 |f| is periodic implies f is periodic Nov 3 '15
6 Every $f : [a, b] → [a, b]$ has a fixed point where $f$ is continuous. Deduce the intermediate value theorem. May 8 '16
6 Is every complete metric space closed? May 7 '16
6 Comparing LU or QR decompositions for solving least squares Dec 2 '16
5 Solve the differential equation $\frac{dy}{dx}=\frac{2x+y}{y}$ Nov 3 '15
5 If $n$ is a product of primes, what is the number of divisors? Dec 17 '15
5 Find complex roots of $\frac{2i}{1+i}$ Jan 18 '16
4 Given $p,q$ odd primes, prove that if $\gcd(a,pq)=1$ then $a^{\operatorname{lcm} (p-1,q-1)} \equiv 1 \pmod {pq}$ Dec 17 '15
4 Solve $x^2\equiv -3\pmod {\!91}$ by CRT lifting roots $\!\bmod 13\ \&\ 7$ Dec 14 '15
4 Show that $\cot \frac{\pi}{2m}\cot \frac{2\pi}{2m}\cot \frac{3\pi}{2m}…\cot \frac{(m-1)\pi}{2m}=1$ Apr 27 '16
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