Year: 2024
Type: article
Abstract: With respect to the 6th problem of the 29th IMO, let b = a + n for the equation of the problem, it gets an equation about a, using the mathematical theory to solve the equation about a, because a > 0, b > 0 in order to obtain a positive root a, the calculation results in k < n2, it demonstrates that k = n2. Moreover, from b = a + n , if a and b take all of the positive integers, n will also take all of the positive or negative integers. Therefore, the paper proves that there are no positive integers a > 0, b > 0 and k > 0 such that a2 + b2/ab + 1 = k is the square of an integer except the case of a = b = 1.
Author: Zhang Yue
Institution: Hunan Normal University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4405382928