Library / /27 of 57

, 2010

Number theory Difficulty 3.0 AMC 10/12 Prove it Canada

Suppose that $p$ is an even integer and that $q$ is an odd integer. Explain why the system of equations $x + y = p$ , $x - y = q$ has no positive integer solutions $(x, y)$ .

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.