Subject: squares and cubes.
Name: Harman Chaudhry
Question: You need to find a and b so that Since 5 divides the left side, 5 must also divide the right side. Since 5 does not divide 3 it must divide b^{5}. But 5 is a prime so if 5 divided b^{5} it must also divide b. Likewise 3 divides the right side so it follows that 3 divides a. Thus the left side must contain 5 3^{3} and the right side must contain 3 5^{5}. To make these equal we need four more 5's on the left side and two more 3's on the right side. That is But 3^{3} 5^{4} is not a cube and 5^{5} 3^{3} is not a fifth power. First fix up the 5's. Multiply both side by 5^{k} so that, on the left 5^{4+k} is a cube and, on the right 5^{5+k} is a fifth power. In a similar fashion fix the 3's When you are done check to see that the number you have has 10 digits. Cheers,Penny
