I try to find a possible integer root for 22P+1 + 2P + 1
Assume: 22P+1 + 2P + 1=( 2p + 2p-1 - 1)^2
expanding the right side and comparing with
the left side we get
w= 0 or w=16
giving p=4 as the only non-negative solution, w=0 is ignored,since w=2P is always positive.
p=0 is a trivial solution.
It seems (maybe a formal proof is required) that there is no other way to factorize 22P+1 + 2P + 1 into two equal factors
Edited on April 26, 2011, 3:36 pm