# The 15th Birthday

Happy Birthday to me, and many thanks to people who helped me in the past year. Let's keep calm and carry on.

# Sol: Leo and the MO Problem

Problem Link: http://oj.hecz.info:4000/problem/2 As the problem instructs, you are supposed to solve this function. $$S_n = \sum_{k=1}^{n} \left[ \dfrac{(3k+6)!+1}{3k+7} - \left[ \dfrac{(3k+6)!}{3k+7} \right] \right]$$ Let's take a look at it, cons…

Fermat's Little Theorem: For a prime number $p$, for any integer $a$, if $\gcd(a,b)=1$, then $a^{p-1}\equiv1(mod p)$ If you want to judge whether p is a prime number, then randomly x in $[2,p-1]$ every time, if $x^{p-1}\not\equiv1$ then $p$ is not …