+150 1)Find the largest prime factor of $3^{15} + 3^{11} + 3^{6} + 1.$
2)Suppose that $p$ and $q$ are prime numbers such that $p$ divides $q+1$ and $q$ divides $p+1.$ Determine $p+q.$
+2862 2) The two prime numbers have to be one away from each other.
So it is 2 and 3.
Lets check:
2 / (3+1)
3/ (2+1)
Yes, so P + Q is 5
+2862 1) The answer is 61
I don't know why though! 
. I brute forced the problem...
1 - Sum them up first: 3^15 + 3^11 + 3^6 + 1=14,526,784
Then factor the sum: 14,526,784 = 2^6×61^3 (9 prime factors, 2 distinct)
As you can see, the largest prime factor is 61.
+2862 That is what I did, but there has to be a trick to do this without a calculator or internet
