This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.
GoalGiven 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
(0, 0, 3, 0, 3)
(1, 0, 2, 2, 4)
(3, 0, 0, 0, 0)
Line 1: An integer n
Line 1: A count of solutions
0 < n < 30 000
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