2018/015) Find all positive n such that $3^{n-1} +5^{n-1} $ divides $3^n + 5^n$

We have $3^n + 5^n= 3(3^{n-1} +5^{n-1}) + 2*5^{n-1}$
So if  $3^{n-1} +5^{n-1} $ divides $3^n +5^n $ then it divides $2*5^{n-1}$
But $3^{n-1} +5^{n-1} $ does not divide $5^{n-1}$ and they are co-primes
So $3^{n-1} +5^{n-1} $ divides 2
So $3^{n-1} +5^{n-1}$ = 1 or 2 so we get n= 1