I try to find a possible integer root for   2^2P+1 + 2^P + 1

Assume:   2^2P+1 + 2^P + 1=( 2^p + 2^p-1 - 1)^2

let   w=2^P

expanding the right side and comparing with

the left side we get 

 4*w=(w^2)/4

w= 0 or w=16

giving  p=4 as the only non-negative solution, w=0 is ignored,since w=2^P  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 2^2P+1 + 2^P + 1 into two equal factors

Edited on April 26, 2011, 3:36 pm

Posted by Ady TZIDON on 2008-07-05 01:22:14