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If f(x) is a function, then we define the function \( f^{(n)}(x)\) to be the result of n applications of f to x, where n is a positive integer. For example, \(f^{(3)}(x)=f(f(f(x))). \)

We define the order of an input x with respect to f to be the smallest positive integer m such that \(f^{(m)}(x)=x. \).

Now suppose f(x) is the function defined as the remainder when x squared is divided by 11. What is the order of 5 with respect to this function f?

 Apr 7, 2022
edited by Guest  Apr 7, 2022
 #1
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The order is 20.

 Apr 7, 2022

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