prove that: x^y=(5x+3y)^(13x+8y)
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.