Something lie that happens in all bases e.g. in base 8 all multiples of 7 add up to 7 (if you keep adding), in hex all multiples of f add up to f, and in binary everything eventually adds up to 1 (except zero).

Similarly, in base 8 7^2 is 61 and in hex f^2 is e1.

(n-1)^2 = n^2 - 2*n + 1 = n(n-2) + 1 which in base n is written with n-2 as the fist digit and 1 as the second digit.