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# Fermat's Last Theorem

After reading Arthur C. Clarke and Frederik Pohl's The Last Theorem,I thought about the problem for a while and I found that the difference between two numbers raised to the power n ( $$c^{n} = (a+b)^{n} - a^{n}$$ ) can be expressed as $$\displaystyle \sum_{i=0}^n b \times a^{n-1} \times ( \frac{a+b}{a} )^{i}$$.So if it can be proved that $$\displaystyle \sum_{i=0}^n b \times a^{n-1} \times ( \frac{a+b}{a} )^{i}$$ cannot be equal to a number raised to the $$n$$th power then this problem could be solved.

Note by Tan Li Xuan
3 years, 8 months ago