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Problem 570

AMC 12 late, AIME early

Number theory Difficulty 5.0 Prove it

8. Prove that the sum of three consecutive natural numbers is divisible by three.

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

Official solution

Instruction. Three consecutive natural numbers can be represented as: $n, \boldsymbol{n}+1, \boldsymbol{n}+2$ .

$s=n+(n+1)+(n+2)=3 n+3=3(n+1)$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.