Competition problem — Number theory

Library / /39 of 48

Number theory Difficulty 5.0 AIME, harder Prove it United States

Problem:
Find all ordered pairs $(m, n)$ of integers such that $231 m^{2} = 130 n^{2}$ .

Solution

Solution:
The unique solution is $(0, 0)$ .

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.