What is the remainder when x^X^x^x... is divided by x-700^(1/700)?

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SUMMARY

The discussion centers on finding the remainder when the infinite power tower \( x^{x^{x^{...}}} \) is divided by \( x - 700^{1/700} \). Participants reference Bézout's theorem in relation to the problem, indicating that the remainder is likely \( 700^{1/700} \) raised to itself infinitely. However, the challenge lies in expressing this remainder as a whole number, as the infinite nature of the power tower complicates direct calculations.

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mathelord
whats the remainder when x^X^x^x... is divided by x-700^(1/700)
leaving answer in whole number
 
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I think it's called Bézout's theorem (you may want to check it out in your textbook,though;it's been a while since i graduated h-s).I have a hunch that,even though the first "polynomial" (the power tower) is infinite,the remainder will be power tower of 700^{\frac{1}{700}},which is a number.

But of course,it doesn't make any sense,this "remainder" cannot be checked upon,because you can't do an infinity of divisions.

Daniel.
 
but my teacher gave us the problem,and said we should leave the answer in whole number not exponent.i guess abia must have posted series of these questions in other forms.so i still need help with it.i know the remainder is in the form (700^1/700)^(700^1/700)...
but it should be a number
 

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