# Project Euler

Project Euler是个很有意思的地方，你可以使用任何方法解决上面的问题，你甚至可以直接通过搜索引擎获得答案，不过，那样就没意思啦。

## 第一题

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000.


列出10以下所有3或5的倍数，我们将得到3，5，6和9。他们的和是23。



$sum(n) = \sum\limits_{i=1}^{\lfloor\frac{n}{3}\rfloor}3i + \sum\limits_{i=1}^{\lfloor\frac{n}{5}\rfloor}5i-\sum\limits_{i=1}^{\lfloor\frac{n}{15}\rfloor}15i$
$\sum\limits_{i=1}^n ki = k\frac{(n)(n+1)}{2}$

## 第二题

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:
1,2,3,5,8,13,21,34,55,89,...
By considering the terms in the Fibonacci sequence whose values do not excedd four million, find the sum of the even-valued terms.


斐波那契数列中的每一项，都是由前两项相加而得。如果从1和2开始，则前面10个元素将会是：
1,2,3,5,8,14,21,34,55,89,...



## 第三题

The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143?


13195的质因数是 5，7，13和29。



###参考资料