1. The problem statement, all variables and given/known data prove that: x^y=(5x+3y)^(13x+8y) 2. Relevant equations 3. The attempt at a solution Can I say that x^y divides both 5x+3y and 13x+8y and go on from there or what? Then in case one u could multiply 5x+3y by 13 and 13x+8y by 5 and do the difference and you'll get that x^y divides y Case 2: multiply 5x+3y by 8 and 13x+8y by 3 and then we get x^y divides x. And from case 1 and case 2 we can conclude that x^y=(5x+3y)^(13x+8y). Note that ^ stands for the greatest common divisor.