k=3, 3=2^1+1
k=4, 6=5^1+1
k=5, 10=3^2+1
k=8, 28=3^3+1
k(k1)/2=p^n+1
k^2k2p^n2=0
quadratic formula
k=.5+.5sqrt(9+8p^n)
I just checked primes up to 100 and powers that kept the discriminant small enough to see whether the square root had a decimal on my calculator. So there may be larger solutions, but if so they are pretty big (or n=1 and p>100).

Posted by Jer
on 20180329 09:29:35 