MathNet 2005 — Part 02 Question 188

Prove: If $4^{n} \cdot 7 = a^{2} + b^{2} + c^{2} + d^{2}$ equals $n, a, b, c, d \in \mathbb{N} \setminus \{0\}$, then none of the square numbers can be less than $4^{n-1}$.