Grades 11-12 Video Solutions 2023-2023_11-12

Video Transcription

Video Summary

The problem involves finding integer pairs \((m, n)\) that satisfy the inequality \(|2m-2023| + |2n-m| \leq 1\). The method involves analyzing conditions where one of the absolute expressions equals 1 and the other 0. The calculation shows that since \(2m\) must be even and 2023 is odd, the expression \(2m - 2023 = 1\) or \(-1\) leads to \(m\) being either 1011 or 1012. However, \(2n = m\) implies \(m\) must be even, leading only to \(m = 1012\) and \(n = 506\). Thus, the only valid pair is \((1012, 506)\).

Keywords

integer pairs

inequality

absolute expressions

even numbers

valid pair