**Exercise 4.**
For each positive integer \(n\), this software gives the order of
\(U(n)\) and the order of each element in \(U(n)\). Do you see any
relationship between the order of \(U(n)\) and the order of its elements?
Run the program for \(n = 8, 16, 32, 64\) and 128. Make a conjecture
about the number of elements of order 4 in \(U(2^k)\) when \(k\) is at
least 3. Make a conjecture about the number of elements of order 4 in
\(U(2^k)\) when \(k\) is at least 4. Make a conjecture about the number
of elements of order 8 is \(U(2^k)\) when \(k\) is at least 5. Make a
conjecture about the maximum order of any element in \(U(2^k)\) when k
is at least 3. Try to find a formula for an element of order 4 in \(U(2^k)\)
when \(k\) is at least 3. Try to find a formula for an element of order 4
in \(U(2^k)\) when \(k\) is at least 4.

Please enter \(n\), the result will show below in the form of member(order).