math [math]Tokyo Institute of Technology, Entrance exam, math, 2019
Problem
\(\displaystyle a = \frac{2^8}{3^4}\)，consider the number sequence $$b_k = \frac{(k+1)^{k+1}}{a^k k!}\ \ (k ...
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math [math]Tokyo Institute of Technology Entrance Exam, Math, 2019
Problem
Let \(H_1, \cdots, H_n\) be distinct \(n\)-planes in the space. Suppose that the space is divided by \(H_1, ...
math [math]Euler関数の和公式
【定理】正の整数\(n\)に対して、\(n\)と互いに素である\(1\)以上\(n\)以下の整数の個数を\(\phi(n)\)とする。これはEulerのTotient関数と呼ばれ、以下が成り立つ。$$\sum_{d\mid n}{\phi...