Project Euler — Problem 46 Solution

Problem

It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.

9 = 7 + 2x12

15 = 7 + 2x22

Project Euler — Problem 47 Solution

Problem

The first two consecutive numbers to have two distinct prime factors are:

14 = 2 x 7

15 = 3 x 5

The first three consecutive numbers to have three…

Project Euler — Problem 44 Solution

Problem

Pentagonal numbers are generated by the formula, Pn=n(3n-1)/2. The first ten pentagonal numbers are:

1, 5, 12, 22, 35, 51, 70, 92, 117, 145, …

It can be seen that P4 + P7 = 22 +…