Find the smallest positive integer that has a remainder of 1 after division by 2, a remainder of 2 after division by 3, a remainder of 3 after division by 4, a remainder of 4 after division by 5, a remainder of 5 after division by 6.

Step-by-step explanation:

The smallest number I found was 59 which certainly is true.

The next one is 119

And a third one in this series is 179

I did this by brute force. In other words, I let a computer do all the counting and dividing.