Positive integers between 1 to 100 inclusive are written on a blackboard, each exactly once. One operation involves choosing two numbers a and b on the blackboard and erasing them, then writing the greatest common divisor of a2+b2+2 and a2b2+3. After a number of operations, there is only one positive integer left on the blackboard. Prove this number cannot be a perfect square. number theorygreatest common divisorinvariant