How to state each individual solution of an expression is evenly divided by n as opposed to their sum being divided by n

Question

Given that for k2n (n=4 and k takes all integer values from 1 to n)

If we want to state the sum of all solutions is evenly divisible by n we write:

n

∑ k2n = 0 (mod n)

k=0

Is there an equally succinct way to state (in one sentence), that each solution taken individually, is evenly divisible by n?

Answer 1

If you mean all the squares are divisible by $n$, you can just say $\forall (k)k^2 \equiv 0 \pmod n$. Is that what you are looking for?