I'm not sure about that, we can also write:
-1*G + 1*G = N*G
-2*G + 2*G = (-1*G - 1*G) + (1*G +1*G) = 2N*G
...
-k*G + k*G = N*K*G
FWIW in modular arithmetic we have compatibility with scaling (for any integer k):
A ≡ B (mod n)
kA ≡ kB (mod n)
In other words all the following values are in congruence relation:
0 ≡ N ≡ 2N ≡ 3N ≡ kN (mod N)