## Exploring Pascal's triangle

### Problem 148

Published on Saturday, 7th April 2007, 02:00 am; Solved by 3198; Difficulty rating: 50%We can easily verify that none of the entries in the first seven rows of Pascal's triangle are divisible by 7:

1 | ||||||||||||

1 | 1 | |||||||||||

1 | 2 | 1 | ||||||||||

1 | 3 | 3 | 1 | |||||||||

1 | 4 | 6 | 4 | 1 | ||||||||

1 | 5 | 10 | 10 | 5 | 1 | |||||||

1 | 6 | 15 | 20 | 15 | 6 | 1 |

However, if we check the first one hundred rows, we will find that only 2361 of the 5050 entries are *not* divisible by 7.

Find the number of entries which are *not* divisible by 7 in the first one billion (10^{9}) rows of Pascal's triangle.