Question 15
a. Does there exist a positive integer $n$ such that the eight last digits of the number $n^2 + 1$ are the same as in the number $2n$, but the ninth digit from the end of these two numbers are different?
b. Does there exist a positive integer $n$ such that the nine last digits of the number $n^2 + 1$ are the same as in the number $2n$, but the tenth digit from the end of these two numbers are different?
b. Does there exist a positive integer $n$ such that the nine last digits of the number $n^2 + 1$ are the same as in the number $2n$, but the tenth digit from the end of these two numbers are different?