such that the relation ![\[|z^{2n}+z^nw^n+w^{2n} | = 2^{2n}+2^n+1 \]](http://latex.artofproblemsolving.com/1/2/2/1229a609403904449c447225094b3d97e063efd4.png)
holds for all positive integers 
.
and 
Prove that
such that 
for reals 
.
such that 
.
Y by
Find all five-digit numbers that satisfy the following conditions:
1. The number is a palindrome.
2. The middle digit is twice the value of the first digit.
3. The number is a perfect square.
Proposed by Tamar Turashvili, Georgia
1. The number is a palindrome.
2. The middle digit is twice the value of the first digit.
3. The number is a perfect square.
Proposed by Tamar Turashvili, Georgia
.
,
.
,
for which this is a 
-
)
as solutions.
