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).