Modulo Arithmetic/Examples/a^2 + (a+2)^2 + (a+4)^2 + 1 Modulo 12

Example of Modulo Arithmetic
Let $a$ be an odd integer.

Then:
 * $a^2 + \paren {a + 2}^2 + \paren {a + 4}^2 + 1 \equiv 0 \pmod {12}$

Proof
Let $a = 2 k + 1$ where $k \in \Z$.

Then:

Hence the result.