Sequence of squares $a^2+b^2=2c^2$
Source: Argentina TST for iberoamerican 2008 Problem 3
August 14, 2008
number theory proposednumber theory
Problem Statement
Show that exists a sequence of terms such that:
1)Every term is a perfect square
2) every term is greater than the one before it ( it is strictly increasing)
3)Every two terms of the sequence are relative prime
4) The average between two consecutive terms is also a perfect square
Daniel