カテゴリー: 数論

\[ P\left(n\right)=1+\sum_{k=1}^{2^{n}}\left\lfloor \sqrt[n]{\frac{n}{\sum_{j=1}^{k}\left\lfloor \cos^{2}\left(\frac{\left(j-1\right)!+1}{j}\pi\right)\right\rfloor }}\right\rfloor \]

\[ QR(p,q)QR(q,p)=\left(-1\right)^{\frac{p-1}{2}\frac{q-1}{2}} \]

\[ QR(a,p)\overset{p}{\equiv}a^{\frac{p-1}{2}} \]

\[ \varphi(p-1) \]

\[ \varphi(p^{n})=p^{n}-p^{n-1} \]

\[ \varphi(n) =\#\left\{ k\in\mathbb{N};1\leq k\leq n,\gcd(k,n)=1\right\} \]

\[ a^{n}\overset{p}{\equiv}1 \]

\[ QR(a,p) \]

\[ ax+by=c \]

\[ ax+by=c\text{が整数解を持つ}\Leftrightarrow c\text{は}\gcd(a,b)\text{の倍数} \]