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**