Suppose that x and y are positive integers such that \(x^2 y^2=46656\) What is the sum of all possible values of x?
Thanks in advance.
+600 Note that \(46656=2^6*3^6\). We take the square root of both sides to get xy=2^3*3^3. So we are essentially finding the sum of the factors of 2^3*3^3. S(2^3*3^3)=S(2^3)*S(3^3). For 2^3 --> 1,2,4,8 --> 15. For 3^3 --> 1,3,9,27 --> 40. So 15*40=600, which is your answer.
