丢番图方程；正整数解；同余；递归序列。
Diophantine equation; Positive integer solution; congruence; Recurrent sequence.
在通过对任一正整数提出另外一种唯一分解式的基础上，利用初等方法得到了关于立方补数的几个有趣的渐近公式。
On the basis of requesting another factorization of an integer in only one way, two interesting asymptotic formulas on cub complements are obtained through the elementary method.
证明了连续正整数的立方和为素数或素数方幂仅有惟一解。
On the prime powers in sums of squares of three consecutive positive integers;
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