A Maple Exploration of Problem 6 of the IMO 88

Zhenbing Zeng, Xiang Sun, Yong Huang, Yaochen Xu, Xiaoru Chen, Lu Yang

Abstract: In this paper, we show that by using Maple software, some direct searching computation could derive a solution to Problem 6 of the 1988 International Mathematics Olympiad, which asks to prove that if a and b are integers such that \(ab+1\) divides \(a^2+b^2\), then \((a^2+b^2)/(ab+1)\) is the square of an integer.