Question 162
Prove that there are infinitely many terms of the arithmetic sequence $1, 14, 27, 40, \dots, 1+13k, \dots$ which are of the form $222\ldots22$. In other words a number that is made up using only the digit $2$.
(Hint: $1001 = 7 \times 11 \times 13$)
(Hint: $1001 = 7 \times 11 \times 13$)