PE1-3

Problem 1

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.

package main

import "fmt"

func main() {
    result := 0
    fmt.Println("1000以内3和5的倍数之和")
    for i := 0; i < =1000; i++ {
        if i%3 == 0 && i%5 == 0 {
            result += i
        }
    }
    fmt.Println(result)
}

结果：233168

Problem 2

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.

package main

import "fmt"

func main() {
   i := 1
   j := 2
   sum := 0
   for {
      temp := i + j
      i = j
      j = temp
      if j%2 == 0 {
         sum += j
      }
      if j > 4000000 {
         break
      }
   }
   fmt.Println(sum + 2)
}

结果：4613732

Problem 3

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

What is the largest prime factor of the number 600851475143 ?

package main

import (
   "fmt"
   "os"
)

func main() {

   a1 := 600851475143
   a2 := 10
   saun(a2, a1)
   fmt.Println(a1)
}

func saun(a2, a1 int) {
   temp := 0
   m := 1
   for i := 2; i < a2; i++ {
      for j := 2; j < i; j++ {
         temp = j
         if i%j == 0 {
            break
         }
      }
      if temp == i-1 {
         if a1%i == 0 {
            if a1/i == 1 {
               fmt.Println(a1)
               os.Exit(0)
            }
            m = a1 / i
            a1 = m
            m = 1
         }
      }
   }
   saun(a2*10, a1)
}

答案：6857