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Zhiwei Sun Squares
Given a positive integer n, find the number of ordered tuples (a, b, c, d, e) over non-negative integers for which a² + b² + c² + d² = n and b + 3c + 5d = e².
Note: A conjecture by 孙智伟 (Sūn, Zhìwěi) states that this count is always at least 1.
For example, if n is 9, there are ...