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

In summary, the conversation discusses the problem of finding the remainder when a power tower with infinite terms is divided by x-700^(1/700). The speaker mentions Bézout's theorem and suggests that the remainder may be the power tower of 700^1/700. However, the concept of finding a remainder for an infinite division does not make sense. The person asking for help clarifies that their teacher has given them this problem and asks for assistance in finding the remainder in whole number form. The summary concludes that the remainder is in the form of a power tower with terms of 700^1/700 but it should be a number.
  • #1
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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  • #2
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 [tex] 700^{\frac{1}{700}} [/tex],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.
 
  • #3
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
 

What is the Remainder Theorem?

The Remainder Theorem is a mathematical concept that states that when a polynomial function is divided by a linear function of the form (x - a), the remainder will be equal to the value of the polynomial at the point x = a.

How is the Remainder Theorem used in polynomial division?

The Remainder Theorem is used to determine the remainder of a polynomial division. It is particularly useful when dealing with long or complex polynomial divisions, as it simplifies the process by reducing the number of steps required.

What is the relationship between the Remainder Theorem and the Factor Theorem?

The Remainder Theorem and the Factor Theorem are closely related. The Factor Theorem states that if a polynomial function has a root at x = a, then (x - a) is a factor of the polynomial. This means that if a function satisfies the Factor Theorem, it will also satisfy the Remainder Theorem.

Can the Remainder Theorem be used to find roots of a polynomial function?

No, the Remainder Theorem cannot be used to find the roots of a polynomial function. It can only be used to determine the remainder of a polynomial division when the divisor is of the form (x - a). To find the roots of a polynomial function, the Factor Theorem or other methods must be used.

Are there any limitations to the Remainder Theorem?

The Remainder Theorem only applies when the divisor is of the form (x - a). It cannot be used for polynomial divisions with divisors of other forms. Additionally, the Remainder Theorem does not work for all polynomial functions, as some may have complex or irrational roots that cannot be evaluated at a single point.

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