When is sin(x) rational?

很久很久以前在學弟那看到一個問題:$\sin1^{\circ}$ ~ $\sin89^{\circ}$ 中只有 $\sin30^{\circ}$ 為有理數。


Given $a > 0, a\neq 1$, $\forall n \in \mathbb{N}$, we have

$$ \frac{1+a^2+a^4+\cdots + a^{2n}}{a+a^3+\cdots+a^{2n-1}} > \frac{n+1}{n} $$


很久以前在 FB 上看到的這題

求證不等式 對於實數 $x$,$\cos(\sin x) > \sin(\cos x)$

LeetCode 0015-3Sum


Given an array nums of n integers, are there elements a, b, c in nums such that a + b + c = 0? Find all unique triplets in the array which gives the sum of zero.

Notice that the solution set must not contain duplicate triplets.