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本文首先研究了X~n尾数域的性质,从而得到了尾数域存在的四种类型为:〔X~(4k-2)〕·,〔X~(4k-1)〕·,〔X~(4k)〕·,(X~(4k+1)〕·;并且得到尾数组合规律,发现满足方程:X~n+Y~n=Z~n的最可能存在整数解的基本域尾数组合数组共有636组。同时,证明了方程有限解与无限解的关系,当n≥3时,方程如果能够找到一组整数解,则容易证明方程具有无穷组整数解。通过X~n的尾数域研究,引出了正整数组合的具体方程(对于负整数组合也同样成立),则不定方程 X~n+Y~n=Z~n即由具体方程式 X~n+(X+a)~n=(X+b)~n所替代;a=C_Y-C_X+10(i_Y-i_X),b=C_Z-C_X+10(i_Z-i_X)。因此即可采用一元n次多项式求取方程X的解数;并根据二项式定理及小数幂的性质即能证明“费尔马大定理”。
In this paper, the properties of X ~ n mantissa fields are studied first, then the four types of mantissa fields are obtained: [X ~ (4k-2)], [X ~ (4k-1) 4k)], (X ~ (4k + 1)] ···, and the law of mantissa is obtained. It is found that the basic mantissa array that satisfies the equation: X ~ n + Y ~ n = Z ~ n is most likely to have integer solution. 636.At the same time, we prove the relationship between the finite solution and the infinite solution.When n≥3, if the equation can find a set of integer solutions, it is easy to prove that the equation has an infinite set of integer solutions.By the X ~ (For the negative integer combination is also true), then the indefinite equation X ~ n + Y ~ n = Z ~ n from the specific equation X ~ n + (X + a) ~ n = (X + a = C_Y-C_X + 10 (i_Y-i_X), b = C_Z-C_X + 10 (i_Z-i_X), so a polynomial of degree n can be used to obtain the solution of equation X. According to Binomial theorem and the nature of the decimal power that can prove “Fermat’s Theorem.”