In this paper, we find out a kind of method of verifying whether an integer is quasi-amicable or not, and prove the Fermat numbers are never perfect or part of an quasi-amicable pair.

为了判断整数是否为拟亲和数，文章在讨论费玛数和数论函数性质的基础上，找到了一种验证一个整数是否是拟亲和数的方法，从而证明了费玛数不与其他正整数构成拟亲和数对的结论。

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However, the famous Fermat's Last Theorem tells us that if the numbers are not squared but, say, multiplied three times (cubed) then no numbers can be found that will work.

BBC: The secret of squares revealed