Individually divisible?
Number Theory
Level
1
I have chosen four integers \({\color{red}a}, {\color{blue}b}, {\color{green}c},\) and \({\color{purple}d}\) so that all five of the following sums are values divisible by 3:
- \({\color{red}a}+{\color{blue}b}+{\color{green}c}\)
- \({\color{red}a}+{\color{blue}b}+{\color{purple}d}\)
- \({\color{red}a}+{\color{green}c}+{\color{purple}d}\)
- \({\color{blue}b}+{\color{green}c}+{\color{purple}d}\)
- \({\color{red}a} + {\color{black}0}+{\color{black}0}. \)
Are \({\color{blue}b},\) \({\color{green}c},\) and \({\color{purple}d}\) also guaranteed to be divisible by 3?
by
Pi Han Goh