Project Euler

Problem 1

Multiples of 3 or 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.

{sum distinct raze 1_'where@' 0=(til x) mod/:3 5}

Problem 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.

sum {x where not x mod 2}{last[x]<4000000} {x,sum -2#x}/(1 1)

Problem 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?