Hi Eric, hope you feel better soon. I would like to write a solution for Question 3.
Assuming x=17n, where n\in\mathbb{Z}. Given x<1000, n+1<60. Since 17n+1 is divisible by 8, so is n+1. The largest possible n is 55, and it makes the largest possible X 935, which is one less than a multiple of 8.
