Grades 11-12 Video Solutions 2014-11&12 Video Solutions 2014 problem27

11&12 Video Solutions 2014 problem27

Video Transcription

Video Summary

The problem involves solving for how many different values the integer \( m \) can take given the equations involving \( k \), \( m \), and \( n \). By analyzing possible values and relationships of \( k \), \( m \), and \( n \), we determine that only two scenarios produce positive integers for \( m \). These occur when \( n = 10 \), \( k = 3 \), and \( n = 5 \), \( k = 5 \). In other options, \( m \) results in negative values and is not possible. Thus, \( m \) can take only two different values, making the answer 2.

Keywords

integer values

equations

positive integers

scenarios

solution