# Have You Seen it Before?

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

Given that $$a, b, n$$ are positive integers such that $$\gcd(a, b)=1$$ and $$n>1,$$ find all solutions $$(a, b, n)$$ to the equation above and enter your answer as $$\sum (a+b+n).$$

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