Find the number of $n$ that follow the following: $ \bigstar $ The number of integers $ (x,y,z) $ following this equation is not a multiple of 4. $ 2n=x^2+2y^2+2x^2+2xy+2yz $
Source: 2024 KJMO first round
Tags: number theory, modular arithmetic
Find the number of $n$ that follow the following: $ \bigstar $ The number of integers $ (x,y,z) $ following this equation is not a multiple of 4. $ 2n=x^2+2y^2+2x^2+2xy+2yz $