Simple Calculus view on Fermat's Last Theorem

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manpreet Tuteehub forum best answer Best Answer 3 years ago

My question (more of a hypothesis really) is basically this: If a function f(x)f(x) is defined such that f(x)f′(x) is not constant and never the same for any 2 values of xx. Then there do not exist positive integers a,b,ca,b,c and abca≤b≤c such that,

 

a0f(x)dx=cbf(x)dx(1)(1)∫0af(x)dx=∫bcf(x)dx

 

Taking f(x)=xnf(x)=xn then

  • for n>1n>1(1)(1) becomes Fermat's Last Theorem, while
  • for n=1n=1n id="MathJax-Span-94" class="mo" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; f
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