MathDB

Positive integers between

1

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

a^2+b^2+2

and

a^2b^2+3

. After a number of operations, there is only one positive integer left on the blackboard. Prove this number cannot be a perfect square.

Problem Statement