费马大定理，解集v6
Fermat's Last Theorem, Solution Sets v6
摘要：
导出了C^n = A^n + B^n的非零整数解集。n = 2的非零整数解集是[C -（a + b）]^2 = 2ab。变量a和b分别等于（C-A）和（C-B），并且是2M^2的非零整数因子，其中M是非零整数。C大于（a + b），因为当C小于（a + b）时，2ab的平方根是虚数。C等于或大于（a + b + 1），因为我们只考虑整数。n = 2的解集的推导适用于n = 3，n = 4，并推广到n。n = n的解集为[C -（a + b）]^n = ab（[n：2]C^（n-2）*（2）- [n：3]C^（n-3）*（3a + 3b）+. + [n：n] {[n：1]a^（n-2）+ [n：2]a^（n-3）*b^1 + [n：3]a^（n-4）*b^2 +. + [n：n-1]b^（n-2）}）。其中，二项式系数[n：r] = n！/ [(n- r）！r！]是二项式幂（1 + x）^n的多项式展开式中x^r项的系数，如果r > n，则[n：r] = 0。将该方程除以[C-（a + b）]^（n-2），得到[C-（a + b）]^2。[C -（a + b）]^2的解集等于2ab。只有当n等于2时，第n个解集才等于2ab。[C -（a + b）]^2（即，当n大于2时，[C-（a + b）]^n除以[C -（a + b）]^（n-2））总是大于2ab。非零整数解只存在于n = 2时。
英文摘要：
The non-zero integer solution set is derived for C^n = A^n + B^n. The non-zero integer solution set for n = 2 is [C - (a + b)]^2 = 2ab. The variables a and b equal (C - A) and (C - B) respectively and are nonzero integer factors of 2M^2 where M is a non-zero integer. C is greater than (a + b) since the square root of 2ab is an imaginary number when C is less than (a + b). C is equal or greater than (a + b + 1) since we are only considering whole numbers. The derivation of the solution set for n = 2 is applied to n = 3, n = 4, and generalized to n. The solution set for n = n is [C - (a + b)]^n = ab([n:2]C^(n-2)*(2) - [n:3]C^(n-3)*(3a + 3b)+ ... + [n:n] {[n:1]a^(n-2) + [n:2]a^(n-3)*b^1 + [n:3]a^(n-4)*b^2 +... + [n:n-1]b^(n-2)}). Where the binomial coefficient [n:r] = n!/[(n - r)!r!] is the coefficient of the x^r term in the polynomial expansion of the binomial power (1 + x)^n and [n:r] = 0 if r > n. Divide this equation by [C-(a + b)]^(n-2) to obtain [C-(a + b)]^2. The solution set for [C - (a + b)]^2 equals 2ab. The nth solution set equals 2ab only when n equals 2. [C - (a + b)]^2 (I.e., [C - (a + b)]^n divided by [C - (a + b)]^(n-2)) is always greater than 2ab when n is greater than 2. Non-zero integer solutions exist only for n = 2.
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