Project Euler | 欧拉计划

Project Euler | 欧拉计划 是一系列需要利用数学和计算机知识及技巧来解答的问题

题面

#1. Multiples of 3 and 5

Multiples of 3 and 5

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.

3的倍数和5的倍数

#2. Even Fibonacci numbers

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 exceed four million, find the sum of the even-valued terms.

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, … 考虑该斐波那契数列中不超过四百万的项，求其中为偶数的项之和。

#3. Largest prime factor

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?

13195的所有质因数为5、7、13和29。

600851475143最大的质因数是多少？

#4. Largest palindrome product

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.

Find the largest palindrome made from the product of two 3-digit numbers.

#5. Smallest multiple

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.

What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

2520是最小的能够被1到10整除的数。