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# Fermat's Last Theorem Redone

How can we prove no Pythagorean Triple can be written as $$({x^{n} ,y^{n},z^{n}})$$ for integer $$x,y,z,n$$ and $$n>1$$ without using Fermat's Last Theorem?

Note that if we could prove this, we would have proven half of Fermat's Last Theorem since $$x^{n}+y^{n}=z^{n}$$ can be written as $$(x^{m})^{2}+(y^{m})^{2}=(z^{m})^{2}$$ for even $$n$$ and $$m>1$$.

Note by Tan Wei Xin
2 years, 4 months ago