# A Fresh Power Diophantine Equation

$a^n-b^{n+2}=(a+b)^{n-1}$

$$a$$ and $$b$$ are relatively prime positive integers and $$n\, (>1)$$ is an integer. Find all solutions to the equation above and enter your answer as $$\sum (a+b+n).$$

This is a generalization of the problem from 1997 Russian Olympiad:

For prime numbers $$p$$ and $$q,$$ solve $$p^3-q^5=(p+q)^2.$$

×