Prove that we can pick $2$ numbers from the set of $4$ numbers $\{a_1,a_2,a_3,a_4\}$ such that their difference is always divisible by $3$.
2026-03-29 12:30:34.1774787434
pigeonhole principle question related to divisability
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We have $3$ possible residues modulo $3$ , namely $0,1,2$. Hence two of the numbers must have the same residue. If we subtract thenm the difference will be divisible by $3$.